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Bernoulli numbers and Zeta functions

Author: Tsuneo Arakawa; Tomoyoshi Ibukiyama; Masanobu Kaneko; Don Zagier
Publisher: Tokyo : Springer, 2014.
Series: Springer monographs in mathematics
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Printed edition:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Tsuneo Arakawa; Tomoyoshi Ibukiyama; Masanobu Kaneko; Don Zagier
ISBN: 9784431549192 4431549196 4431549188 9784431549185
OCLC Number: 884435975
Description: 1 online resource (xi, 274 pages) : illustrations (some color).
Contents: 1. Bernoulli numbers --
2. Stirling numbers and Bernoulli numbers --
3. Theorem of Clausen and von Staudt, and Kummer's congruence --
4. Generalized Bernoulli numbers --
5. The Euler-Maclaurin summation formula and the Riemann Zeta function --
6. Quadratic forms and ideal theory of quadratic fields --
7. Congruence between Bernoulli numbers and class numbers of imaginary quadratic fields --
8. Character sums and Bernoulli numbers --
9. Special values and complex integral representation of L-functions --
10. Class number formula and an easy Zeta function of the space of quadratic forms --
11. [rho]-adic measure and Kummer's congruence --
12. Hurwitz numbers --
13. The Barnes multiple Zeta function --
14. Poly-Bernoulli numbers --
Appendix : curious and exotic identities for Bernoulli numbers / Don Zagier.
Series Title: Springer monographs in mathematics
Responsibility: Tsuneo Arakawa, Tomoyoshi Ibukiyama, Masanobu Kaneko ; with an appendix by Don Zagier.

Abstract:

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. a formula for  Read more...

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"The book touches on all of thewell-known classical results related to Bernoulli numbers and zeta functions .... The book will offer something to readers at all levels of expertise, from thestudent Read more...

 
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