TWISTS OF AUTOMORPHIC L-FUNCTIONS AT THE CENTRAL POINT

Hung M. Bui

Type: Article

Publication Date: 2013-01-10

Citations: 1

DOI: https://doi.org/10.1142/s1793042113500115

Abstract

We study the nonvanishing of twists of automorphic L-functions at the center of the critical strip. Given a primitive character χ modulo D satisfying some technical conditions, we prove that the twisted L-functions L(f.χ, s) do not vanish at s = ½ for a positive proportion of primitive forms of weight 2 and level q, for large prime q. We also investigate the central values of high derivatives of L(f.χ, s), and from that derive an upper bound for the average analytic rank of the studied L-functions.

Locations

International Journal of Number Theory - View
arXiv (Cornell University) - View - PDF

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+	Random Matrix Theory and L-Functions at s = 1/2	2000	Jonathan P. Keating N. C. Snaith
+	Newforms and functional equations	1975	Wen Ch ing Winnie Li
+ PDF Chat	Non-vanishing of high derivatives of automorphic L-functions at the center of the critical strip	2000	Emmanuel Kowalski Philippe Michel Jeffrey M. VanderKam
+ PDF Chat	Applications of the<i>L</i>-functions ratios conjectures	2007	J. Brian Conrey N. C. Snaith
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+	The critical order of vanishing of automorphicL-functions with large level	1995	William Duke