On the zeros of the L-function associated with the cubic theta function

Abstract

The paper considers the function defined by the Dirichlet series

$$L(\tau ;s) = \sum\limits_\nu {\frac{{\tau (\nu )}}{{\left\| \nu \right\|^s }}} , s \in \mathbb{C}$$

, where τ(ν) is the νth Fourier coefficient of the cubic Kubota-Patterson theta function. The zeros of the function L(τ ·) in the domain |Im s| < 444 are computed. Bibliography: 4 titles.