By Tsuneo Arakawa,Tomoyoshi Ibukiyama,Masanobu Kaneko,Don B. Zagier
Two significant topics are handled during this publication. the most one is the idea of Bernoulli numbers and the opposite is the speculation of zeta features. traditionally, Bernoulli numbers have been brought to provide formulation for the sums of powers of consecutive integers. the genuine cause that they're critical for quantity conception, notwithstanding, lies within the indisputable fact that specific values of the Riemann zeta functionality might be written by utilizing Bernoulli numbers. This results in extra complicated subject matters, a couple of that are handled during this ebook: old feedback on Bernoulli numbers and the formulation for the sum of powers of consecutive integers; a formulation for Bernoulli numbers by way of Stirling numbers; the Clausen–von Staudt theorem at the denominators of Bernoulli numbers; Kummer's congruence among Bernoulli numbers and a similar conception of p-adic measures; the Euler–Maclaurin summation formulation; the sensible equation of the Riemann zeta functionality and the Dirichlet L capabilities, and their exact values at compatible integers; quite a few formulation of exponential sums expressed by way of generalized Bernoulli numbers; the relation among excellent periods of orders of quadratic fields and equivalence sessions of binary quadratic varieties; classification quantity formulation for optimistic yes binary quadratic varieties; congruences among a few category numbers and Bernoulli numbers; easy zeta services of prehomogeneous vector areas; Hurwitz numbers; Barnes a number of zeta services and their particular values; the useful equation of the doub
le zeta services; and poly-Bernoulli numbers. An appendix via Don Zagier on curious and unique identities for Bernoulli numbers is usually provided. This e-book could be relaxing either for amateurs and for pro researchers. as the logical family among the chapters are loosely hooked up, readers can commence with any bankruptcy reckoning on their pursuits. The expositions of the subjects aren't continuously common, and a few elements are thoroughly new.
Read or Download Bernoulli Numbers and Zeta Functions (Springer Monographs in Mathematics) PDF
Similar number theory books
This booklet presents a self-contained review of the function of conformal teams in geometry and mathematical physics. It contains a cautious improvement of the fabric, from the fundamentals of Clifford algebras to extra complicated issues. each one bankruptcy covers a particular point of conformal teams and conformal spin geometry.
Ce livre contient une démonstration détaillée et complète de l'existence d'un isomorphisme équivariant entre les excursions p-adiques de Lubin-Tate et de Drinfeld. Le résultat est établi en égales et inégales caractéristiques. Il y est également donné comme program une démonstration du fait que les cohomologies équivariantes de ces deux excursions sont isomorphes, un résultat qui a des functions à l'étude de l. a. correspondance de Langlands locale.
This can be the 1st introductory publication on a number of zeta features and a number of polylogarithms that are the generalizations of the Riemann zeta functionality and the classical polylogarithms, respectively, to the a number of variable surroundings. It includes all of the uncomplicated recommendations and the real houses of those capabilities and their precise values.
This ebook collects greater than thirty contributions in reminiscence of Wolfgang Schwarz, such a lot of which have been awarded on the 7th foreign convention on effortless and Analytic quantity conception (ELAZ), held July 2014 in Hildesheim, Germany. starting from the idea of arithmetical features to diophantine difficulties, to analytic elements of zeta-functions, some of the examine and survey articles conceal the vast pursuits of the well known quantity theorist and adored colleague Wolfgang Schwarz (1934-2013), who contributed over 100 articles on quantity concept, its background and comparable fields.
- Computation with Linear Algebraic Groups (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)
- Additive Number Theory: Festschrift In Honor of the Sixtieth Birthday of Melvyn B. Nathanson
- Probabilistic Diophantine Approximation: Randomness in Lattice Point Counting (Springer Monographs in Mathematics)
- Arne Beurling und Hitlers Geheimschreiber: Schwedische Entzifferungserfolge im 2. Weltkrieg (German Edition)
- Partial Differential Equations in Physics: 6 (Pure and Applied Mathematics)
Additional resources for Bernoulli Numbers and Zeta Functions (Springer Monographs in Mathematics)
Bernoulli Numbers and Zeta Functions (Springer Monographs in Mathematics) by Tsuneo Arakawa,Tomoyoshi Ibukiyama,Masanobu Kaneko,Don B. Zagier