Titlebook: Bernoulli Numbers and Zeta Functions; Tsuneo Arakawa,Tomoyoshi Ibukiyama,Masanobu Kaneko Book 2014 Springer Japan 2014 Bernoulli numbers a

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The Barnes Multiple Zeta Function,In this chapter, we introduce Barnes’ multiple zeta function, which is a natural generalization of the Hurwitz zeta function, give an analytic continuation, and then express their special values at negative integers by using Bernoulli polynomials.

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Poly-Bernoulli Numbers,In this chapter, we define and study a generalization of Bernoulli numbers referred to as poly-Bernoulli numbers, which is a different generalization than the generalized Bernoulli numbers introduced in Chap. 4.

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https://doi.org/10.1007/978-4-431-54919-2Bernoulli numbers and polynomials; L-functions; MSC; 11B68, 11B73, 11M06, 11L03, 11M06, 11M32, 11M35; R

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The Relevance of Medicine in Footballl part” of .. is given by the following theorem. This result gives a foundation for studying .-adic properties of the Bernoulli numbers. It also plays a fundamental role in the theory of .-adic modular forms through the Eisenstein series [82].

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Interviews with Injured Athletes so-called prehomogeneous vector spaces. We also prove a class number formula of imaginary quadratic fields. Before that, we review the theory of multiplicative structure of ideals of quadratic field without proof.

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Structural properties of families,e Bernoulli numbers in connection to the study of the sums of powers of consecutive integers .. After listing the formulas for the sums of powers. up to .?=?10 (Bernoulli expresses the right-hand side without factoring), he gives a general formula involving the numbers which are known today as Berno

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The Relevance of Medicine in Footballl part” of .. is given by the following theorem. This result gives a foundation for studying .-adic properties of the Bernoulli numbers. It also plays a fundamental role in the theory of .-adic modular forms through the Eisenstein series [82].

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Marta Massada,Gino Kerkoffs,Paulo Amado Dirichlet character, which we define at the beginning of the first section. Bernoulli polynomials are generalizations of Bernoulli numbers with an indeterminate. These two generalizations are related, and they will appear in various places in the following chapters.