On Calculations of Zeros of Various L-functions

Abstract

As we have shown several years ago [Y2], zeros of $L(s, \Delta )$ and $L^(2)(s, \Delta )$ can be calculated quite efficiently by a certain experimental method. Here $\Delta$ denotes the cusp form of weight 12 with respect to SL$(2, Z)$ and $L(s, \Delta )$ (resp. $L^(2)(s, \Delta )$) denotes the standard (resp. symmetric square) $L$-function attached to $\Delta$. The purpose of this paper is to show that this method can be applied to a wide class of $L$-functions so that we can obtain precise numerical values of their zeros.