ON CALCULATIONS OF ZEROS OF VARIOUS L-FUNCTIONS

Hiroyuki Yoshida

Abstract. As we have shown several years ago [Y2], zeros of L(s, Δ) and L^{(}2)(s, Δ) can be calculated quite efficiently by a certain experimental method. Here Δ denotes the cusp form of weight 12 with respect to SL(2, Z) and L(s, Δ) (resp. L^{(}2)(s, Δ)) denotes the standard (resp. symmetric square) L-function attached to Δ. 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.

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