By Tsuneo Arakawa,Tomoyoshi Ibukiyama,Masanobu Kaneko,Don B. Zagier

Two significant matters are taken care of during this booklet. the most one is the speculation of Bernoulli numbers and the opposite is the speculation of zeta capabilities. traditionally, Bernoulli numbers have been brought to provide formulation for the sums of powers of consecutive integers. the true cause that they're crucial for quantity idea, even though, lies within the incontrovertible fact that unique values of the Riemann zeta functionality may be written by utilizing Bernoulli numbers. This ends up in extra complex issues, a couple of that are handled during this booklet: old comments on Bernoulli numbers and the formulation for the sum of powers of consecutive integers; a formulation for Bernoulli numbers by means of Stirling numbers; the Clausen–von Staudt theorem at the denominators of Bernoulli numbers; Kummer's congruence among Bernoulli numbers and a similar idea of *p*-adic measures; the Euler–Maclaurin summation formulation; the practical equation of the Riemann zeta functionality and the Dirichlet L features, and their detailed values at appropriate 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; category quantity formulation for confident certain binary quadratic kinds; congruences among a few type numbers and Bernoulli numbers; uncomplicated zeta capabilities of prehomogeneous vector areas; Hurwitz numbers; Barnes a number of zeta capabilities and their exact values; the practical equation of the doub

le zeta features; and poly-Bernoulli numbers. An appendix via Don Zagier on curious and unique identities for Bernoulli numbers can also be provided. This publication should be stress-free either for amateurs and for pro researchers. as the logical family members among the chapters are loosely hooked up, readers can commence with any bankruptcy counting on their pursuits. The expositions of the subjects aren't continuously commonplace, and a few elements are thoroughly new.

**Read or Download Bernoulli Numbers and Zeta Functions (Springer Monographs in Mathematics) PDF**

**Best number theory books**

Graph partitioning is a theoretical topic with functions in lots of parts, mostly: numerical research, courses mapping onto parallel architectures, snapshot segmentation, VLSI layout. over the past forty years, the literature has strongly elevated and large advancements were made. This e-book brings jointly the information amassed in the course of a long time to extract either theoretical foundations of graph partitioning and its major functions.

**Concise Computer Mathematics: Tutorials on Theory and Problems (SpringerBriefs in Computer Science)**

Tailored from a modular undergraduate direction on computational arithmetic, Concise laptop arithmetic grants an simply available, self-contained creation to the elemental notions of arithmetic valuable for a working laptop or computer technological know-how measure. The textual content displays the necessity to speedy introduce scholars from quite a few academic backgrounds to a few crucial mathematical options.

**Algebraic Number Theory (Springer Undergraduate Mathematics Series)**

The technical problems of algebraic quantity concept frequently make this topic seem tricky to rookies. This undergraduate textbook presents a welcome technique to those difficulties because it offers an approachable and thorough advent to the subject. Algebraic quantity concept takes the reader from specified factorisation within the integers via to the modern day quantity box sieve.

The realm round us is saturated with numbers. they're a primary pillar of our sleek society, and authorized and used with rarely a moment notion. yet how did this scenario grow to be? during this e-book, Leo Corry tells the tale in the back of the assumption of quantity from the early days of the Pythagoreans, up till the flip of the 20 th century.

- Conformal Groups in Geometry and Spin Structures: 50 (Progress in Mathematical Physics)
- A Field Guide to Algebra (Undergraduate Texts in Mathematics)
- Number Theory in Science and Communication: With Applications in Cryptography, Physics, Digital Information, Computing, and Self-Similarity: 7 (Springer Series in Information Sciences)
- Discourses on Algebra (Universitext)

**Extra info for Bernoulli Numbers and Zeta Functions (Springer Monographs in Mathematics)**

**Sample text**