On the values of the Epstein zeta function
- 1 February 1973
- journal article
- research article
- Published by Cambridge University Press (CUP) in Glasgow Mathematical Journal
- Vol. 14 (1) , 1-12
- https://doi.org/10.1017/s001708950000166x
Abstract
Let ζ(s) = σn-s(Res >1) denote the Riemann zeta function; then, as is well known,, whereBmdenotes themth Bernoulli number, In this paper we investigate the possibility of similar evaluations of the Epstein zeta function ζq(s) at the rational integerss = k> 2. Let be a positive definite quadratic form and where the summation is over all pairs of integers except (0, 0). In attempting to evaluate ζq(k) we are guided by Kronecker's first limit formula [11] where γ is Euler's constant, is the Dedekind eta-function, and τ is the complex number in the upper half plane, ℋ, associated with Q by the formula On the basis of (1.3) we would expect a formula involving functions of τ. This formula is stated in Theorem 1, (2.13).Keywords
This publication has 1 reference indexed in Scilit:
- Lectures on Modular Forms. (AM-48)Published by Walter de Gruyter GmbH ,1962