منابع مشابه
Recurrence for values of the zeta function
Using the Padé approximation of the exponential function, we obtain a general recurrence relation for values of the zeta function which contains, as particular cases, many of relations already proved. Applications to Bernoulli polynomials are given. At last, we derive some new recurrence relations with gap of length 4 for zeta numbers. MSC: 11B68 41A21
متن کاملIrrationality of Values of Zeta-function
1. Introduction. The irrationality of values of the zeta-function ζ(s) at odd integers s ≥ 3 is one of the most attractive problems in number theory. Inspite of a deceptive simplicity and more than two-hundred-year history of the problem, all done in this direction can easily be counted. It was only 1978, when Apéry [A] obtained the irrationality of ζ(3) by a presentation of " nice " rational a...
متن کاملMultiple Zeta Values over Global Function Fields
Abstract. Let K be a global function field with finite constant field Fq of order q. In this paper we develop the analytic theory of a multiple zeta function Zd(K; s1, . . . , sd) in d independent complex variables defined over K. This is the function field analog of the Euler-Zagier multiple zeta function ζd(s1, . . . , sd) of depth d ([Z1]). Our main result is that Zd(K; s1, . . . , sd) has a...
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We investigate a few types of generalizations of the Hurwitz zeta function, written Z(s, a) in this abstract, where s is a complex variable and a is a parameter in the domain that depends on the type. In the easiest case we take a ∈ R, and one of our main results is that Z(−m, a) is a constant times Em(a) for 0 ≤ m ∈ Z, where Em is the generalized Euler polynomial of degree n. In another case, ...
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We explain work on the arithmetic of Gamma and Zeta values for function fields. We will explore analogs of the gamma and zeta functions, their properties, functional equations, interpolations, their special values, their connections with periods of Drinfeld modules and t-motives, algebraic relations they satisfy and various methods showing that there are no more relations between them. We also ...
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ژورنال
عنوان ژورنال: Applied Numerical Mathematics
سال: 2010
ISSN: 0168-9274
DOI: 10.1016/j.apnum.2010.05.011