Distribution of zeros and zero-density estimates for the derivatives of L-functions attached to cusp forms

2014/02/16 by Yoshikatsu Yashiro, Yashiro, Yoshikatsu
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #math.NT

paper · pdf · doi:10.48550/arxiv.1402.3800

21 pages

arxiv created 2014/07/03 · arxiv updated 2014/07/04

Abstract

Let f be a holomorphic cusp form of weight k with respect to SL₂(ℤ) which is a normalized Hecke eigenform, L_f(s) the L-function attached to the form f. In this paper, we shall give the relation of the number of zeros of L_f(s) and 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.

Cited by

• Approximate functional equation and mean value formula for the derivatives of L-functions attached to cusp forms

Related

• Zero-density estimates for L-functions attached to cusp forms
• On the density hypothesis for L-functions associated with holomorphic cusp forms
• Approximate functional equation and mean value formula for the derivatives of L-functions attached to cusp forms
• A zero-density estimate for L-functions associated with \rm GL(3) Hecke--Maass cusp forms
• Non-vanishing of L-functions associated to cusp forms of half-integral weight