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Dirichlet eta function $\eta (s)$ in the complex plane. The color of a point $s$ encodes the value of $\eta (s)$. Strong colors denote values close to zero and hue encodes the value's argument.

In mathematics, in the area of analytic number theory, the Dirichlet eta function is defined by the following Dirichlet series, which converges for any complex number having real part > 0:

$\eta (s)=\sum _{n=1}^{\mathrm{\infty }}\frac{(-1{)}^{n-1}}{n^s}=\frac{1}{1^s}-\frac{1}{2^s}+\frac{1}{3^s}-\frac{1}{4^s}+\cdots$

This Dirichlet series is the alternating sum corresponding to the Dirichlet series expansion of the Riemann zeta function, ζ(s) — and for this reason the Dirichlet eta function is also known as the alternating zeta function, also denoted ζ*(s). The following simple relation holds:

$\eta (s)=(1-2^{1-s})\zeta (s)$

While the Dirichlet series expansion for the eta function is convergent only for any complex number s with real part > 0, it is Abel summable for any complex number. This serves to define the eta function as an entire function (and the above relation then shows the zeta function is meromorphic with a simple pole at s = 1, and perhaps poles at the other zeros of the factor $1-2^{1-s}$).

Equivalently, we may begin by defining

$\eta (s)=\frac{1}{\Gamma (s)}{\int }_0^{\mathrm{\infty }}\frac{x^{s-1}}{e^x+1}dx$

which is also defined in the region of positive real part. This gives the eta function as a Mellin transform.

Hardy gave a simple proof of the functional equation for the eta function, which is

$\eta (-s)=2\frac{1-2^{-s-1}}{1-2^{-s}}{\pi }^{-s-1}s\sin \left(\frac{\pi s}{2}\right)\Gamma (s)\eta (s+1).$

From this, one immediately has the functional equation of the zeta function also, as well as another means to extend the definition of eta to the entire complex plane.

Zeros

The zeros of the eta function include all the zeros of the zeta function: the infinity of negative even integers (real equidistant simple zeros); an infinity of zeros along the critical line, none of which are known to be multiple and over 40% of which have been proven to be simple, and the hypothetical zeros in the critical strip but not on the critical line, which if they do exist must occur at the vertices of rectangles symmetrical around the x-axis and the critical line and whose multiplicity is unknown. In addition, the factor $1-2^{1-s}$ adds an infinity of complex simple zeros, located at equidistant points on the line $\mathrm{\Re }(s)=1$, at $s_n=1+2n\pi i/\log (2)$ where n is any nonzero integer.

Under the Riemann hypothesis, the zeros of the eta function would be located symmetrically with respect to the real axis on two parallel lines $\mathrm{\Re }(s)=1/2,\mathrm{\Re }(s)=1$, and on the perpendicular half line formed by the negative real axis.

Landau's problem with ζ(s) = η(s)/0 and solutions

In the equation η(s) = (1−2^1−s) ζ(s), "the pole of ζ(s) at s=1 is cancelled by the zero of the other factor" (Titchmarsh, 1986, p. 17), and as a result η(1) is neither infinite nor zero. However, in the equation

$\zeta (s)=\frac{\eta (s)}{1-2^{1-s}},$

η must be zero at all the points $s_n=1+n\frac{2\pi }{\ln 2}i,n\ne 0,n\in Z$, where the denominator is zero, if the Riemann zeta function is analytic and finite there. The problem of proving this without defining the zeta function first was signaled and left open by E. Landau in his 1909 treatise on number theory: "Whether the eta series is different from zero or not at the points $s_n\ne 1$, i.e., whether these are poles of zeta or not, is not readily apparent here."

A first solution for Landau's problem was published almost 40 years later by D. V. Widder in his book The Laplace Transform. It uses the next prime 3 instead of 2 to define a Dirichlet series similar to the eta function, which we will call the $\lambda$ function, defined for $\mathrm{\Re }(s)>0$ and with some zeros also on $\mathrm{\Re }(s)=1$, but not equal to those of eta. Template:Hidden begin

$\begin{array}{c}\lambda (s)=(1-\frac{3}{3^s})\zeta (s)=(1+\frac{1}{2^s})-\frac{2}{3^s}+(\frac{1}{4^s}+\frac{1}{5^s})-\frac{2}{6^s}+\dots \end{array}$

If $s$ is real and strictly positive, the series converges since the regrouped terms alternate in sign and decrease in absolute value to zero. According to a theorem on uniform convergence of Dirichlet series first proven by Cahen in 1894, the $\lambda (s)$ function is then analytic for $\mathrm{\Re }(s)>0$, a region which includes the line $Re(s)=1$. Now we can define correctly, where the denominators are not zero,

$\zeta (s)=\frac{\eta (s)}{1-\frac{2}{2^s}}$

or

$\zeta (s)=\frac{\lambda (s)}{1-\frac{3}{3^s}}$

Since $\frac{\log 3}{\log 2}$ is irrational, the denominators in the two definitions are not zero at the same time except for $s=1$, and the $\zeta (s)$ function is thus well defined and analytic for $\mathrm{\Re }(s)>0$ except at $s=1$. We finally get indirectly that $\eta (s_n)=0$ when $s_n\ne 1$:

$\eta (s_n)=(1-\frac{2}{2^{s_n}})\zeta (s_n)=\frac{1-\frac{2}{2^{s_n}}}{1-\frac{3}{3^{s_n}}}\lambda (s_n)=0.$

An elementary direct and $\zeta$-independent proof of the vanishing of the eta function at $s_n\ne 1$ was published by J. Sondow in 2003. It expresses the value of the eta function as the limit of special Riemann sums associated to an integral known to be zero, using a relation between the partial sums of the Dirichlet series defining the eta and zeta functions for $\mathrm{\Re }(s)>1$.

Template:Hidden begin With some simple algebra performed on finite sums, we can write for any complex s

${\eta }_{2n}(s)=\sum _{k=1}^{2n}\frac{(-1{)}^{k-1}}{k^s}=1-\frac{1}{2^s}+\frac{1}{3^s}-\frac{1}{4^s}+\dots +\frac{(-1{)}^{2n-1}}{{(2n)}^s}=1+\frac{1}{2^s}+\frac{1}{3^s}+\frac{1}{4^s}+\dots +\frac{1}{{(2n)}^s}-2(\frac{1}{2^s}+\frac{1}{4^s}+\dots +\frac{1}{{(2n)}^s})$

$=(1-\frac{2}{2^s}){\zeta }_{2n}(s)+\frac{2}{2^s}(\frac{1}{{(n+1)}^s}+\dots +\frac{1}{{(2n)}^s})=(1-\frac{2}{2^s}){\zeta }_{2n}(s)+\frac{2n}{{(2n)}^s}\frac{1}{n}(\frac{1}{{(1+1/n)}^s}+\dots +\frac{1}{{(1+n/n)}^s}).$

Now if $s=1+it$ and $2^s=2$, the factor multiplying ${\zeta }_{2n}(s)$ is zero, and

${\eta }_{2n}(s)=\frac{1}{n^{it}}{R}_n(\frac{1}{{(1+x)}^s},0,1),$

where Rn(f(x),a,b) denotes a special Riemann sum approximating the integral of f(x) over [a,b]. For t = 0 i.e. s = 1, we get

$\eta (1)=\underset{n\to \mathrm{\infty }}{lim}{\eta }_{2n}(1)=\underset{n\to \mathrm{\infty }}{lim}{R}_n(\frac{1}{1+x},0,1)={\int }_0^1\frac{dx}{1+x}=\log 2\ne 0.$

Otherwise, if $t\ne 0$, then $|n^{1-s}|=|n^{-it}|=1$, which yields

$|\eta (s)|=\underset{n\to \mathrm{\infty }}{lim}|{\eta }_{2n}(s)|=\underset{n\to \mathrm{\infty }}{lim}|R_n(\frac{1}{{(1+x)}^s},0,1)|=|{\int }_0^1\frac{dx}{{(1+x)}^s}|=|\frac{2^{1-s}-1}{1-s}|=|\frac{1-1}{-it}|=0.$

Assuming $\eta (s_n)=0$, for each point $s_n\ne 1$ where $2^{s_n}=2$, we can now define $\zeta (s_n)$ by continuity as follows,

$\zeta (s_n)=\underset{s\to s_n}{lim}\frac{\eta (s)}{1-\frac{2}{2^s}}=\underset{s\to s_n}{lim}\frac{\eta (s)-\eta (s_n)}{\frac{2}{2^{s_n}}-\frac{2}{2^s}}=\underset{s\to s_n}{lim}\frac{\eta (s)-\eta (s_n)}{s-s_n}\frac{s-s_n}{\frac{2}{2^{s_n}}-\frac{2}{2^s}}=\frac{{\eta }^{\prime }(s_n)}{\log (2)}.$

The apparent singularity of zeta at $s_n\ne 1$ is now removed, and the zeta function is proven to be analytic everywhere in $\mathrm{\Re }s>0$, except at $s=1$ where

$\underset{s\to 1}{lim}(s-1)\zeta (s)=\underset{s\to 1}{lim}\frac{\eta (s)}{\frac{1-2^{1-s}}{s-1}}=\frac{\eta (1)}{\log 2}=1.$

Integral representations

A number of integral formulas involving the eta function can be listed. The first one follows from a change of variable of the integral representation of the Gamma function (Abel, 1823), giving a Mellin transform which can be expressed in different ways as a double integral (Sondow, 2005). This is valid for $\mathrm{\Re }s>0.$

$\begin{array}{cc}\Gamma (s)\eta (s)& ={\int }_0^{\mathrm{\infty }}\frac{x^{s-1}}{e^x+1}dx={\int }_0^{\mathrm{\infty }}{\int }_0^x\frac{x^{s-2}}{e^x+1}dydx\\ & ={\int }_0^{\mathrm{\infty }}{\int }_0^{\mathrm{\infty }}\frac{(t+r{)}^{s-2}}{e^{t+r}+1}drdt={\int }_0^1{\int }_0^1\frac{(-\log (xy){)}^{s-2}}{1+xy}dxdy.\end{array}$

The Cauchy–Schlömilch transformation (Amdeberhan, Moll et al., 2010) can be used to prove this other representation, valid for $\mathrm{\Re }s>-1$. Integration by parts of the first integral above in this section yields another derivation.

$2^{1-s}\Gamma (s+1)\eta (s)=2{\int }_0^{\mathrm{\infty }}\frac{x^{2s+1}}{{\cosh }^2(x^2)}dx={\int }_0^{\mathrm{\infty }}\frac{t^s}{{\cosh }^2(t)}dt.$

The next formula, due to Lindelöf (1905), is valid over the whole complex plane, when the principal value is taken for the logarithm implicit in the exponential.

$\eta (s)={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}\frac{(1/2+it{)}^{-s}}{e^{\pi t}+e^{-\pi t}}dt.$

This corresponds to a Jensen (1895) formula for the entire function $(s-1)\zeta (s)$, valid over the whole complex plane and also proven by Lindelöf.

$(s-1)\zeta (s)={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}\frac{(1/2+it{)}^{1-s}}{(e^{\pi t}+e^{-\pi t}{)}^2}dt.$

"This formula, remarquable by its simplicity, can be proven easily with the help of Cauchy's theorem, so important for the summation of series" wrote Jensen (1895). Similarly by converting the integration paths to contour integrals one can obtain other formulas for the eta function, such as this generalisation (Milgram, 2012, formula 2.9) stated to be valid for $0<c<1$ and all $s$ :

$\eta (s)=\frac{1}{2}{\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}\frac{(c+it{)}^{-s}}{\sin (\pi (c+it))}dt.$

The zeros on the negative real axis are factored out cleanly by making $c\to 0^{+}$ (Milgram, 2012, formula 3.9) stated to be valid for $\mathrm{\Re }s<0$ :

$\eta (s)=-\sin (s\pi /2){\int }_0^{\mathrm{\infty }}\frac{t^{-s}}{\sinh (\pi t)}dt.$

Numerical algorithms

Most of the series acceleration techniques developed for alternating series can be profitably applied to the evaluation of the eta function. One particularly simple, yet reasonable method is to apply Euler's transformation of alternating series, to obtain

$\eta (s)=\sum _{n=0}^{\mathrm{\infty }}\frac{1}{2^{n+1}}\sum _{k=0}^n(-1{)}^k(\genfrac{}{}{0ex}{}{n}{k})\frac{1}{(k+1{)}^s}.$

Note that the second, inside summation is a forward difference.

Borwein's method

Peter Borwein used approximations involving Chebyshev polynomials to produce a method for efficient evaluation of the eta function. If

$d_k=n\sum _{i=0}^k\frac{(n+i-1)!4^i}{(n-i)!(2i)!}$

then

$\eta (s)=-\frac{1}{d_n}\sum _{k=0}^{n-1}\frac{(-1{)}^k(d_k-d_n)}{(k+1{)}^s}+{\gamma }_n(s),$

where for $\mathrm{\Re }(s)\ge \frac{1}{2}$ the error term γ_n is bounded by

$|{\gamma }_n(s)|\le \frac{3}{(3+\sqrt{8}{)}^n}(1+2|\mathrm{\Im }(s)|)\exp (\frac{\pi }{2}|\mathrm{\Im }(s)|).$

The factor of $3+\sqrt{8}\approx 5.8$ in the error bound indicates that the Borwein series converges quite rapidly as n increases.

Particular values

• η(0) = ¹⁄₂, the Abel sum of Grandi's series 1 − 1 + 1 − 1 + · · ·.
• η(−1) = ¹⁄₄, the Abel sum of 1 − 2 + 3 − 4 + · · ·.
• For k an integer > 1, if B_k is the k-th Bernoulli number then

  $\eta (1-k)=\frac{2^k-1}{k}{B}_k.$

Also:

$\eta (1)=\ln 2$, this is the alternating harmonic series

$\eta (2)=\frac{{\pi }^2}{12}$ Physiotherapist Rave from Cobden, has hobbies and interests which includes skateboarding, commercial property for sale developers in singapore and coin collecting. May be a travel freak and in recent years made a journey to Wet Tropics of Queensland.

$\eta (4)=\frac{7{\pi }^4}{720}\approx 0.94703283$

$\eta (6)=\frac{31{\pi }^6}{30240}\approx 0.98555109$

$\eta (8)=\frac{127{\pi }^8}{1209600}\approx 0.99623300$

$\eta (10)=\frac{73{\pi }^{10}}{6842880}\approx 0.99903951$

$\eta (12)=\frac{1414477{\pi }^{12}}{1307674368000}\approx 0.99975769$

The general form for even positive integers is:

$\eta (2n)=(-1{)}^{n+1}\frac{B_{2n}{\pi }^{2n}(2^{2n-1}-1)}{(2n)!}.$

Derivatives

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${\eta }^{\prime }(s)=\sum _{n=1}^{\mathrm{\infty }}\frac{(-1{)}^n\ln n}{n^s}=2^{1-s}\ln 2\zeta (s)+(1-2^{1-s}){\zeta }^{\prime }(s)$.

${\eta }^{\prime }(1)=\ln (2)\gamma -\ln (2{)}^2/2$

References

• One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
  
  In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
  
  Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
  
  Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
  
  A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
  
  The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
  
  There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
• Landau, Edmund, Handbuch der Lehre von der Verteilung der Primzahlen, Erster Band, Berlin, 1909, p. 160. (Second edition by Chelsea, New York, 1953, p. 160, 933)
• Titchmarsh, E. C. (1986). The Theory of the Riemann Zeta Function, Second revised (Heath-Brown) edition. Oxford University Press.
• One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
  
  In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
  
  Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
  
  Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
  
  A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
  
  The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
  
  There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
• Borwein, P., An Efficient Algorithm for the Riemann Zeta Function, Constructive experimental and nonlinear analysis, CMS Conference Proc. 27 (2000), 29–34.
• Template:Cite arxiv Amer. Math. Monthly 112 (2005) 61–65, formula 18.
• Template:Cite arxiv Amer. Math. Monthly, 110 (2003) 435–437.
• Template:Cite web
• Template:Cite arxiv p. 12.
• Template:Cite arxiv.