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Zeros of the Derivatives of L-functions Attached to Cusp Forms

Yashiro Y.

Bulletin of the Polish Academy of Sciences. Mathematics

2016

Vol. 64, no. 2/3

147--164

Let f be a holomorphic cusp form of weight k with respect to SL2(Z) which is a normalized Hecke eigenform, and Lf(s) the L-function attached to f. We shall give a relation between the number of zeros of Lf(s) and of the derivatives of Lf(s) using Berndt’s method, and an estimate of zero-density of the derivatives of Lf(s) based on Littlewood’s method.