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Results tagged with nt.number-theory
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user 49208
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
3
votes
A new generalisation of Fermat's little theorem?
In this paper (in Russian) : http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=mp&paperid=238&option_lang=eng
there are discussion of this result, including theorem of Gauss, generalization to …
- 1,560
0
votes
1
answer
473
views
Sum of digits of a power [closed]
Are there any explicit formula for a sum of digits for a power in the given base? A problem to be specific: find a sum of digits for a number $2^{100}$ in the system with a base 5. In the system with …
- 1,560
7
votes
Accepted
A (likely) positivity property of the Lerch zeta-function
From Prudnikov,Brychkov,Marichev Integral and Series, Vol.1, sect. 5.4.3, formula 1 we derive that
$$
\sum_{k=0}^\infty \frac{\cos(ak)}{(k+1/2)^{p+1}}=
\frac{1}{\Gamma(s)}\int_0^{\infty}\frac{t^p e^{- …
- 1,560
7
votes
Kuznetsov trace formula, orthogonality of Bessel functions
I was acquainted with Nikolay Vasil'evich Kuznetsov while worked in Vladivostok, 1990s. And he was very kind to mee, too. He tought me that many asymptotics for Bessel functions are not valid, many f …
- 1,560
5
votes
Is this a rational function?
In Prudnikov, Brychkov, Marichev, vol. 1 there is an explicit formula via basic hypergeometric functions. Not rational.
- 1,560