Magnetic moment: Difference between revisions

Latest revision as of 18:24, 1 December 2014

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-In [[mathematics]], the '''Stoneham numbers''' are a certain class of [[real number]]s, named after [[mathematician]] [[Richard G. Stoneham]] (1920–1996). For [[coprime]] numbers ''b'', ''c'' &gt; 1, the Stoneham number &alpha;<sub>''b'',''c''</sub> is defined as
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-:<math>\alpha_{b,c} = \sum_{n=c^k>1} \frac{1}{b^nn} = \sum_{k=1}^\infty \frac{1}{b^{c^k}c^k}</math>
-It was shown by Stoneham in 1973 that &alpha;<sub>''b'',''c''</sub> is ''b''-[[normal number|normal]] whenever ''c'' is an odd [[prime number|prime]] and ''b'' is a [[primitive root modulo n|primitive root]] of ''c''<sup>2</sup>.
-== References ==
-{{reflist}}
-*{{cite book | last=Bugeaud | first=Yann | title=Distribution modulo one and Diophantine approximation | series=Cambridge Tracts in Mathematics | volume=193 | location=Cambridge | publisher=[[Cambridge University Press]] | year=2012 | isbn=978-0-521-11169-0 | zbl=pre06066616 }}
-*{{cite journal | zbl=0276.10028 | last=Stoneham | first=R.G. | title=On absolute $(j,ε)$-normality in the rational fractions with applications to normal numbers | journal=[[Acta Arithmetica]] | volume=22 | pages=277–286 | year=1973 }}
-*{{cite journal | zbl=0276.10029 | last=Stoneham | first=R.G. | title=On the uniform ε-distribution of residues within the periods of rational fractions with applications to normal numbers | journal=[[Acta Arithmetica]] | volume=22 | pages=371–389 | year=1973 }}
-{{numtheory-stub}}
-[[Category:Number theory]]
-[[Category:Sets of real numbers]]

Magnetic moment: Difference between revisions

Latest revision as of 18:24, 1 December 2014

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