# Minimal theta functions

@article{Montgomery1988MinimalTF, title={Minimal theta functions}, author={Hugh L. Montgomery}, journal={Glasgow Mathematical Journal}, year={1988}, volume={30}, pages={75 - 85} }

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 be Rankin [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, let This function satisfies the functional equation (This may be proved by using the formula (4) below, and then twice applying the identity (8).)

## 98 Citations

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