Values of zeta functions at negative integers, Dedekind sums and toric geometry

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...

Dedekind Sums and Values of L-functions at Positive Integers

In this paper, we study Dedekind sums and we connect them to the mean values of Dirichlet L-functions. For this, we introduce and investigate higher order dimensional Dedekind-Rademacher sums given by the expression Sd( −→ a0 , −→ m0) = 1 a0 0 a0−1 ∑

A symbolic approach to multiple zeta values at negative integers

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

Generating functions and generalized Dedekind sums

We study sums of the form ∑ ζ R(ζ), where R is a rational function and the sum is over all nth roots of unity ζ (often with ζ = 1 excluded). We call these generalized Dedekind sums, since the most well-known sums of this form are Dedekind sums. We discuss three methods for evaluating such sums: The method of factorization applies if we have an explicit formula for ∏ ζ(1− xR(ζ)). Multisection ca...

Values of the Riemann zeta function at integers