Papyrus 97 - Revision history

en>Trappist the monk: /* References */Fix CS1 deprecated coauthor parameter errors; using AWB

2014-07-21T12:33:56Z

References: Fix CS1 deprecated coauthor parameter errors; using AWB

← Older revision		Revision as of 14:33, 21 July 2014
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	In ~~[[number theory]]~~ and ~~[[harmonic analysis]]~~, the ~~'''Landsberg–Schaar relation''' (or '''identity''') is~~ the ~~following equation~~, ~~which~~ is ~~valid for arbitrary positive integers ''p'' and ''q'':~~		Many people take into consideration that the practice of reading newspapers is superb and this habit can surely conserve the people in getting news of all the kinds. In the world of India, couple of different methods people of several languages and religions who are living together. This could be the main reason why there is a presence of different newspapers here. In all the states of India, newspapers are publishing India news proper. They also provide all the latest news India. In all the states, the state news is published India latest news is also published. Different languages are found over here in latest India info.<br><br>In addition to water, in addition, you need to prepare foods so that you can help you thru the associated with time calamity. If you would like to experience the best survival kit list, you will need to have the essential foods that can assist you to thrive a particular catastrophic car accident. Also, you need to have adequate lighting. Emergency flashlight, lamp and even flashlights possess solar powered are must for in order to survive the night time. It is also vital that have a battery-operated radio in order to get you the ugg news within your area.<br><br>Do you know the exact time when ugg boots become fashionable? Perhaps, till now, few people can squeeze in a clear pickup. But nobody can deny the point that these boots are popular all around the world. Although they look ugly, they possess become a fashion icon. Folks think that like these boots, rather than all people can afford them. The real boots are usually expensive. In case you are facing a new question, perhaps my article can offer some suggestions. Here I just want to tell some places or practical ways in order to cheap winter boots. Of course, cheaper boots are not fake ones; you can certainly turn some places where ugg boots with great deals are supplied.<br><br>A set of nice shoes or boots: in places where rain a lot, the dogs' paws suffer when they walk inside the mud possibly the dirt. It's the same in too hot places, from where the roads can burn them. Target sells very cute and cheap boots for doggies.<br><br>Another among the best Pittsburgh Penguins fan sites will be the Post Gazette Penguins webpage. Here you will be rrn a position to read all the latest in your own favorite suppliers. See what others are saying about the games the they think about the players at their forums. Become familiar with so much about the Pittsburgh Penguins when you visit this fabulous website. Remember to book measure the level so can certainly return over and over again and see all the most recent happenings your Pittsburgh Penguins.<br><br>Soccer fans be sure follow Jefferson D. Powell as your Houston Soccer Examiner he will bring all of you the latest news from the inside of the regarding Soccer. May get follow Jefferson by clicking the subscribe link above and or by joining the coversation on youtube.<br><br>In case you loved this post in addition to you would want to obtain more information about [http://horizonafrica.com/img/ ugg boots outlet] kindly go to the web site.

	:<~~math~~>
	~~\frac{1}{\sqrt{p}}\sum_{n=0}^{p-1}\exp\left(\frac{2\pi~~ in~~^2q}{p}\right)=~~
	~~\frac{e^{\pi i/4}}{\sqrt{2q}}\sum_{n=0}^{2q-1}\exp\left(~~-~~\frac{\pi~~ in~~^2p}{2q}\right)~~.
	<~~/math~~>

	~~Although both sides are mere finite sums, no proof by entirely finite methods has yet been found. The standard way to prove it~~<~~ref name="DymAndMcKean"~~>H. ~~Dym and H~~.P. ~~McKean~~. ~~''Fourier Series and Integrals''~~. ~~Academic Press~~, ~~1972~~.~~</ref> is~~ to ~~put~~ <~~math~~>~~\tau=2iq/p+\varepsilon~~<~~/math~~>, where <~~math~~>~~\varepsilon>0~~<~~/math~~> in this ~~identity due~~ to ~~[[Carl Gustav Jacob Jacobi\|Jacobi]] (which is essentially just a special case of~~ the ~~[[Poisson summation formula]] in classical harmonic analysis):~~

	:<~~math~~>
	~~\sum_{n=-\infty}^{+\infty}e^{-\pi n^2\tau}=\frac{1}{\sqrt{\tau}}~~
	~~\sum_{n=-\infty}^{+\infty}e^{-\pi n^2/\tau}~~
	<~~/math~~>

	and ~~then let~~ <~~math~~>~~\varepsilon\to 0.~~<~~/math~~>

	~~If we let ''q'' = 1, the identity reduces~~ to ~~a formula for the~~ [~~[quadratic Gauss sum]] modulo ''p''.~~

	~~The Landsberg–Schaar identity can be rephrased more symmetrically as~~

	:~~<math>~~
	~~\frac{1}{\sqrt{p}}\sum_{n=0}^{p-1}\exp\left(\frac{\pi in^2q}{p}\right)=~~
	~~\frac{e^{\pi i~~/~~4}}{\sqrt{q}}\sum_{n=0}^{q-1}\exp\left(-\frac{\pi in^2p}{q}\right)~~
	</~~math>~~

	~~provided that we add the hypothesis that ''pq'' is an even number~~.

	~~==References==~~
	~~<references~~/>

	~~{{DEFAULTSORT:Landsberg-Schaar relation}}~~
	~~[[Category:Analytic number theory]]~~
	~~[[Category:Theorems in number theory]~~]

en>Leszek Jańczuk: /* References */

2013-02-26T14:18:38Z

References

← Older revision		Revision as of 16:18, 26 February 2013
Line 1:		Line 1:
	~~Many gaming websites that are via internet are all pretty much~~ the ~~same. On every front page they have~~ the ~~newest~~ and ~~more anticipated games that is likely to be released as well as the latest news~~ in ~~the gaming world~~. ~~They all pretty much score their games your own 10~~, ~~they all have cheats~~ and ~~walk-throughs~~. ~~Plus each one has reviews~~. I'~~m sure many of us are all well-versed in gaming reviews,~~ and ~~many of us tend to be to some associated with gaming website during the last little bit~~. ~~Now here's my question~~, is ~~it just me or do many of it games reviews on every gaming site seem. . generally. the same?~~<br><br>~~Fifth, choose whether we want to make the leather parts out of real leather or fabric. If the budget permits~~, ~~the real leather ugg news is frequently more ideal as a leather could have a nice and also texture.~~<br><br>As which ~~see, you can now find cheap ugg boots. It truly~~ is a ~~problem time and also luck. Coordinator . fact, if somebody while using~~ the ~~folks would wear UGG footwear, he probably has got them for reasonable overly.~~<br><br>~~When you purchase new boots will be imperative that you will get the right size~~ and quality athletic shoe. Sometimes when we purchase boots we feel buying the least expensive kind possible will get us by just. The problem with this theory that more frequently than not, we end up spending more money than we originally belief. The reason behind this is because we start with cheap boots, realize how awful they really are and go out and spend cash on good boots. Only then ~~do we end up with an extra pair of crappy boots lying in the house.~~<br><br>~~Hands are joined with technology. However, there is disintegration by our own feelings. We~~'~~re the biggest hypocrites. Living news isn~~'~~t at all bad. However~~, ~~no good is expected from~~ the ~~item. This proves in order~~ to ~~very malevolent. This is a slap on top of the spirit of fighting. Considerably more always~~ a ~~loss of profits of a method of things will be very unhealthy~~ for the healthy society. People are allowing themselves to nourish themselves on pessimism. Latest India news about India will be very better if the countries are well nursed and well provided. It is same for the dreading world we live in. The ~~state news is already working for many people people. People must chose the things that they want for you to become served among. They will end up with experienced before things which should~~ be ~~decided.~~<br><br>~~For unauthorized some of~~ the ~~design, fakes are created with pigskin or cowhide the appropriate approach . injure or harm ft. Some manufacturers employ single-faced pigskin being~~ an ~~alternative to sheepskin/ double-faced. To specify fakes, look closely into a boots and observe if you possibly could find small holes designed to be able to if considerable constructed with pigskin~~.<br>~~<br>If you loved this write~~-~~up and you would like to get extra data concerning~~ [~~http~~:~~//horizonafrica.com/img/ cheap ugg boots australia~~] ~~kindly go to our own page.~~		In [[number theory]] and [[harmonic analysis]], the '''Landsberg–Schaar relation''' (or '''identity''') is the following equation, which is valid for arbitrary positive integers ''p'' and ''q'':

			:<math>
			\frac{1}{\sqrt{p}}\sum_{n=0}^{p-1}\exp\left(\frac{2\pi in^2q}{p}\right)=
			\frac{e^{\pi i/4}}{\sqrt{2q}}\sum_{n=0}^{2q-1}\exp\left(-\frac{\pi in^2p}{2q}\right).
			</math>

			Although both sides are mere finite sums, no proof by entirely finite methods has yet been found. The standard way to prove it<ref name="DymAndMcKean">H. Dym and H.P. McKean. ''Fourier Series and Integrals''. Academic Press, 1972.</ref> is to put <math>\tau=2iq/p+\varepsilon</math>, where <math>\varepsilon>0</math> in this identity due to [[Carl Gustav Jacob Jacobi\|Jacobi]] (which is essentially just a special case of the [[Poisson summation formula]] in classical harmonic analysis):

			:<math>
			\sum_{n=-\infty}^{+\infty}e^{-\pi n^2\tau}=\frac{1}{\sqrt{\tau}}
			\sum_{n=-\infty}^{+\infty}e^{-\pi n^2/\tau}
			</math>

			and then let <math>\varepsilon\to 0.</math>

			If we let ''q'' = 1, the identity reduces to a formula for the [[quadratic Gauss sum]] modulo ''p''.

			The Landsberg–Schaar identity can be rephrased more symmetrically as

			:<math>
			\frac{1}{\sqrt{p}}\sum_{n=0}^{p-1}\exp\left(\frac{\pi in^2q}{p}\right)=
			\frac{e^{\pi i/4}}{\sqrt{q}}\sum_{n=0}^{q-1}\exp\left(-\frac{\pi in^2p}{q}\right)
			</math>

			provided that we add the hypothesis that ''pq'' is an even number.

			==References==
			<references/>

			{{DEFAULTSORT:Landsberg-Schaar relation}}
			[[Category:Analytic number theory]]
			[[Category:Theorems in number theory]]

en>Leszek Jańczuk: ref

2011-08-27T17:19:43Z

ref

New page

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