Bernoulli Numbers and Zeta Functions

種類:

電子ブック

責任表示:

by Tsuneo Arakawa, Tomoyoshi Ibukiyama, Masanobu Kaneko

出版情報:

Tokyo : Springer Japan : Imprint: Springer, 2014

著者名:

• Arakawa, Tsuneo
• Ibukiyama, Tomoyoshi
• Kaneko, Masanobu
• SpringerLink (Online service)

シリーズ名:

Springer Monographs in Mathematics ;

ISBN:

9784431549192 [4431549196]    

注記:

Two major subjects are treated in this book. The main one is the theory of Bernoulli numbers and the other is the theory of zeta functions. Historically, Bernoulli numbers were introduced to give formulas for the sums of powers of consecutive integers. The real reason that they are indispensable for number theory, however, lies in the fact that special values of the Riemann zeta function can be written by using Bernoulli numbers. This leads to more advanced topics, a number of which are treated in this book: Historical remarks on Bernoulli numbers and the formula for the sum of powers of consecutive integers; a formula for Bernoulli numbers by Stirling numbers; the Clausen–von Staudt theorem on the denominators of Bernoulli numbers; Kummer's congruence between Bernoulli numbers and a related theory of p-adic measures; the Euler–Maclaurin summation formula; the functional equation of the Riemann zeta function and the Dirichlet L functions, and their special values at suitable integers; various formulas of expo

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