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Simultaneous nonvanishing of products of L-functions associated to elliptic cusp forms

Title
Simultaneous nonvanishing of products of L-functions associated to elliptic cusp forms
Authors
CHOIE, YOUNG JUWinfried KohnenYichao Zhang
Date Issued
15-Jun-2020
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Abstract
A generalized Riemann hypothesis states that all zeros of the completed Hecke L-function L* (f, s) of a normalized Hecke eigenform f on the full modular group should lie on the vertical line Re(s) = k/2. It was shown in [6] that there exists a Hecke eigenform f of weight k such that L* (f , s) not equal 0 for sufficiently large k and any point on the line segments Im(s) = t(0), k-1/2 < Re(s) < k/2 - epsilon, k/2 < Re(s) < k+1/2, for any given real number to and t(0) positive real number epsilon. This paper concerns the non-vanishing of the product L* (f , s)L* (f, w) (s, w is an element of C) on average. (C) 2020 Elsevier Inc. All rights reserved.
Keywords
SERIES
URI
http://oasis.postech.ac.kr/handle/2014.oak/100916
ISSN
0022-247X
Article Type
Article
Citation
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol. 486, no. 2, 2020-06-15
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최영주CHOIE, YOUNG JU
Dept of Mathematics
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