Zeros of the Derivatives of $L$-functions Attached to Cusp Forms
Volume 64 / 2016
Bulletin Polish Acad. Sci. Math. 64 (2016), 147-164
MSC: Primary 11M26; Secondary 11N75.
DOI: 10.4064/ba8068-10-2016
Published online: 27 October 2016
Abstract
Let $f$ be a holomorphic cusp form of weight $k$ with respect to $\mathrm {SL}_2(\mathbb {Z})$ which is a normalized Hecke eigenform, and $L_f(s)$ the $L$-function attached to $f$. We shall give a relation between the number of zeros of $L_f(s)$ and of the derivatives of $L_f(s)$ using Berndt’s method, and an estimate of zero-density of the derivatives of $L_f(s)$ based on Littlewood’s method.
