On the values of a zeta function at nonpositive integers

Values of the Riemann zeta function at integers

A symbolic approach to multiple zeta values at negative integers

Article history: Received 25 October 2015 Accepted 1 December 2016 Available online xxxx

Recurrence for values of the zeta function

Using the Padé approximation of the exponential function, we obtain a general recurrence relation for values of the zeta function which contains, as particular cases, many of relations already proved. Applications to Bernoulli polynomials are given. At last, we derive some new recurrence relations with gap of length 4 for zeta numbers. MSC: 11B68 41A21

On the Difference of Values of the Kernel Function at Consecutive Integers

For each positive integer n, set γ(n) = p|n p. Given a fixed integer k ≠ ±1, we establish that if the ABC-conjecture holds, then the equation γ(n + 1) − γ(n) = k has only finitely many solutions. In the particular cases k = ±1, we provide a large family of solutions for each of the corresponding equations. 1. Introduction. Comparing values of an arithmetic function at consecutive integers is a ...

Values of Zeta Functions at Negative Integers, Dedekind Sums and Toric Geometry

In the present paper, we study relations among special values of zeta functions of real quadratic fields, properties of generalized Dedekind sums and Todd classes of toric varieties. The main theme of the paper is the use of toric geometry to explain in a conceptual way properties of the values of zeta functions and Dedekind sums, as well as to provide explicit computations. Both toric varietie...