The first moment of L-functions of primitive forms on Γ0(pα) and a basis of old forms

JOURNAL OF NUMBER THEORY

卷:131

Article

Ichihara, Yumiko

关键词: Automorphic L-function;    Non-vanishing;   

DOI  :  10.1016/j.jnt.2010.07.012

来源: Elsevier

【 摘 要 】

We consider the first moment of. the value of automorphic L-functions at an arbitrary point on the critical line, a sum over primitive forms weighted by their Petersson's norm. In this paper, we obtain an asymptotic formula for it when weight k is an even integer satisfying 0 < k < 12 or k = 14 and level is p(alpha), where p is a prime number. This formula yields a lower bound of the number of primitive forms, whose L-functions do not vanish at that point. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free