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## Bernoulli numbers and Zeta functions [electronic resource]

자료유형
E-Book(소장)
개인저자
Arakawa, Tsuneo, 1949-2003. Ibukiyama, Tomoyoshi. Kaneko, Masanobu.
서명 / 저자사항
Bernoulli numbers and Zeta functions [electronic resource] / Tsuneo Arakawa, Tomoyoshi Ibukiyama, Masanobu Kaneko.
발행사항
Tokyo :   Springer Japan :   Imprint: Springer,   2014.
형태사항
1 online resource (xi, 274 p.) : ill. (some col.).
총서사항
Springer monographs in mathematics,1439-7382
ISBN
9784431549192
요약
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 exponential sums expressed by generalized Bernoulli numbers; the relation between ideal classes of orders of quadratic fields and equivalence classes of binary quadratic forms; class number formula for positive definite binary quadratic forms; congruences between some class numbers and Bernoulli numbers; simple zeta functions of prehomogeneous vector spaces; Hurwitz numbers; Barnes multiple zeta functions and their special values; the functional equation of the double zeta functions; and poly-Bernoulli numbers. An appendix by Don Zagier on curious and exotic identities for Bernoulli numbers is also supplied. This book will be enjoyable both for amateurs and for professional researchers. Because the logical relations between the chapters are loosely connected, readers can start with any chapter depending on their interests. The expositions of the topics are not always typical, and some parts are completely new.
일반주기
Title from e-Book title page.
서지주기
Includes bibliographical references and index.
이용가능한 다른형태자료
Issued also as a book.
일반주제명
Bernoulli numbers. Functions, Zeta.
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 000 00000nam u2200205 a 4500 001 000046050453 005 20201021142704 006 m d 007 cr 008 201005s2014 ja a ob 001 0 eng d 020 ▼a 9784431549192 040 ▼a 211009 ▼c 211009 ▼d 211009 050 0 0 ▼a QA246 082 0 4 ▼a 512.7/3 ▼2 23 084 ▼a 512.73 ▼2 DDCK 090 ▼a 512.73 100 1 ▼a Arakawa, Tsuneo, ▼d 1949-2003. 245 1 0 ▼a Bernoulli numbers and Zeta functions ▼h [electronic resource] / ▼c Tsuneo Arakawa, Tomoyoshi Ibukiyama, Masanobu Kaneko. 260 ▼a Tokyo : ▼b Springer Japan : ▼b Imprint: Springer, ▼c 2014. 300 ▼a 1 online resource (xi, 274 p.) : ▼b ill. (some col.). 336 ▼a text ▼b txt ▼2 rdacontent 337 ▼a computer ▼b c ▼2 rdamedia 338 ▼a online resource ▼b cr ▼2 rdacarrier 490 1 ▼a Springer monographs in mathematics, ▼x 1439-7382 500 ▼a Title from e-Book title page. 504 ▼a Includes bibliographical references and index. 520 ▼a 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 exponential sums expressed by generalized Bernoulli numbers; the relation between ideal classes of orders of quadratic fields and equivalence classes of binary quadratic forms; class number formula for positive definite binary quadratic forms; congruences between some class numbers and Bernoulli numbers; simple zeta functions of prehomogeneous vector spaces; Hurwitz numbers; Barnes multiple zeta functions and their special values; the functional equation of the double zeta functions; and poly-Bernoulli numbers. An appendix by Don Zagier on curious and exotic identities for Bernoulli numbers is also supplied. This book will be enjoyable both for amateurs and for professional researchers. Because the logical relations between the chapters are loosely connected, readers can start with any chapter depending on their interests. The expositions of the topics are not always typical, and some parts are completely new. 530 ▼a Issued also as a book. 538 ▼a Mode of access: World Wide Web. 650 0 ▼a Bernoulli numbers. 650 0 ▼a Functions, Zeta. 700 1 ▼a Ibukiyama, Tomoyoshi. 700 1 ▼a Kaneko, Masanobu. 830 0 ▼a Springer monographs in mathematics. 856 4 0 ▼u https://oca.korea.ac.kr/link.n2s?url=http://dx.doi.org/10.1007/978-4-431-54919-2 945 ▼a KLPA 991 ▼a E-Book(소장)

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