The Resource Bernoulli numbers and Zeta functions, Tsuneo Arakawa, Tomoyoshi Ibukiyama, Masanobu Kaneko ; with an appendix by Don Zagier
Bernoulli numbers and Zeta functions, Tsuneo Arakawa, Tomoyoshi Ibukiyama, Masanobu Kaneko ; with an appendix by Don Zagier
Resource Information
The item Bernoulli numbers and Zeta functions, Tsuneo Arakawa, Tomoyoshi Ibukiyama, Masanobu Kaneko ; with an appendix by Don Zagier represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Bernoulli numbers and Zeta functions, Tsuneo Arakawa, Tomoyoshi Ibukiyama, Masanobu Kaneko ; with an appendix by Don Zagier represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 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 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 Clausenvon Staudt theorem on the denominators of Bernoulli numbers; Kummer's congruence between Bernoulli numbers and a related theory of [rho]adic measures; the EulerMaclaurin 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 polyBernoulli 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
 Language
 eng
 Extent
 xi, 274 pages
 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 EulerMaclaurin 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 Lfunctions
 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. PolyBernoulli numbers
 Appendix : curious and exotic identities for Bernoulli numbers / Don Zagier
 Isbn
 9784431549185
 Label
 Bernoulli numbers and Zeta functions
 Title
 Bernoulli numbers and Zeta functions
 Statement of responsibility
 Tsuneo Arakawa, Tomoyoshi Ibukiyama, Masanobu Kaneko ; with an appendix by Don Zagier
 Language
 eng
 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 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 Clausenvon Staudt theorem on the denominators of Bernoulli numbers; Kummer's congruence between Bernoulli numbers and a related theory of [rho]adic measures; the EulerMaclaurin 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 polyBernoulli 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
 Cataloging source
 BTCTA
 http://library.link/vocab/creatorDate
 19492003
 http://library.link/vocab/creatorName
 Arakawa, Tsuneo
 Illustrations
 illustrations
 Index
 index present
 Literary form
 non fiction
 Nature of contents
 bibliography
 http://library.link/vocab/relatedWorkOrContributorDate
 1951
 http://library.link/vocab/relatedWorkOrContributorName

 Ibukiyama, Tomoyoshi
 Kaneko, Masanobu
 Zagier, Don
 Series statement
 Springer Monographs in Mathematics,
 http://library.link/vocab/subjectName

 Bernoulli numbers
 Functions, Zeta
 Label
 Bernoulli numbers and Zeta functions, Tsuneo Arakawa, Tomoyoshi Ibukiyama, Masanobu Kaneko ; with an appendix by Don Zagier
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 volume
 Carrier category code

 nc
 Carrier MARC source
 rdacarrier.
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent.
 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 EulerMaclaurin 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 Lfunctions  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. PolyBernoulli numbers  Appendix : curious and exotic identities for Bernoulli numbers / Don Zagier
 Control code
 876005668
 Dimensions
 25 cm
 Extent
 xi, 274 pages
 Isbn
 9784431549185
 Lccn
 2014938983
 Media category
 unmediated
 Media MARC source
 rdamedia.
 Media type code

 n
 Other physical details
 illustrations (some color)
 System control number
 (OCoLC)876005668
 Label
 Bernoulli numbers and Zeta functions, Tsuneo Arakawa, Tomoyoshi Ibukiyama, Masanobu Kaneko ; with an appendix by Don Zagier
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 volume
 Carrier category code

 nc
 Carrier MARC source
 rdacarrier.
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent.
 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 EulerMaclaurin 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 Lfunctions  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. PolyBernoulli numbers  Appendix : curious and exotic identities for Bernoulli numbers / Don Zagier
 Control code
 876005668
 Dimensions
 25 cm
 Extent
 xi, 274 pages
 Isbn
 9784431549185
 Lccn
 2014938983
 Media category
 unmediated
 Media MARC source
 rdamedia.
 Media type code

 n
 Other physical details
 illustrations (some color)
 System control number
 (OCoLC)876005668
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