A lemma about the Epstein zeta-function
- 1 January 1964
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Glasgow Mathematical Association
- Vol. 6 (4) , 198-201
- https://doi.org/10.1017/s2040618500035024
Abstract
Let h (m, n) = αm2 + 2δmn + βn2 be a positive definite quadratic form with determinant αβ–δ2 = 1. It may be put in the shapewith y > 0. We write (for s > 1)The function Zn(s) may be analytically continued over the whole s-plane. Its only singularity is a simple pole with residue π at s = 1.Keywords
This publication has 3 references indexed in Scilit:
- On a problem of Rankin about the Epstein zeta-functionProceedings of the Glasgow Mathematical Association, 1959
- A Minimum Problem for the Epstein Zeta-FunctionProceedings of the Glasgow Mathematical Association, 1953
- Zur Theorie allgemeiner ZetafunctionenMathematische Annalen, 1903