منابع مشابه
18.785F17 Number Theory I Lecture 16 Notes: Riemann’s Zeta Function and the Prime Number Theorem
We now divert our attention from algebraic number theory to talk about zeta functions and L-functions. As we shall see, every global field has a zeta function that is intimately related to the distribution of its primes. We begin with the zeta function of the rational field Q, which we will use to prove the prime number theorem. We will need some basic results from complex analysis, all of whic...
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This result is deduced from the following result. Call an admissible set to be a finite set of integers H which avoids at least one residue class modulo p for each prime p. For any natural number k0, let Q(k0) denote the assertion that for any admissible set H of integers of cardinality k0, there are infinitely many translates n +H of H that contain at least two primes. Note that if H is an adm...
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Are there infinitely many prime pairs with given even difference? Most mathematicians think so. Using a strong arithmetic hypothesis, Goldston, Pintz and Yildirim have recently shown that there are infinitely many pairs of primes differing by at most sixteen. There is extensive numerical support for the prime-pair conjecture (PPC) of Hardy and Littlewood [G.H. Hardy, J.E. Littlewood, Some probl...
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We define p-adic multiple zeta and log gamma functions using multiple Volkenborn integrals, and develop some of their properties. Although our functions are close analogues of classical Barnes multiple zeta and log gamma functions and have many properties similar to them, we find that our p-adic analogues also satisfy reflection functional equations which have no analogues to the complex case. ...
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Stimulated by earlier work by Moll and his coworkers [1], we evaluate various basic log Gamma integrals in terms of partial derivatives of Tornheim– Witten zeta functions and their extensions arising from evaluations of Fourier series. In particular, we fully evaluate
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2016
ISSN: 0035-7596
DOI: 10.1216/rmj-2016-46-5-1701