Minimal theta functions
- 1 January 1988
- journal article
- research article
- Published by Cambridge University Press (CUP) in Glasgow Mathematical Journal
- Vol. 30 (1) , 75-85
- https://doi.org/10.1017/s0017089500007047
Abstract
Let be a positive definite binary quadratic form with real coefficients and discriminant b2 − 4ac = −1.Among such forms, let . The Epstein zeta function of f is denned to beRankin [7], Cassels [1], Ennola [5], and Diananda [4] between them proved that for every real s > 0,We prove a corresponding result for theta functions. For real α > 0, letThis function satisfies the functional equation(This may be proved by using the formula (4) below, and then twice applying the identity (8).)Keywords
This publication has 5 references indexed in Scilit:
- On a problem about the Epstein zeta-functionMathematical Proceedings of the Cambridge Philosophical Society, 1964
- Notes on two lemmas concerning the Epstein zeta-functionProceedings of the Glasgow Mathematical Association, 1964
- A lemma about the Epstein zeta-functionProceedings of the Glasgow Mathematical Association, 1964
- 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