TWISTS OF AUTOMORPHIC L-FUNCTIONS AT THE CENTRAL POINT

被引：1

作者：

Bui, H. M. ^{[1
]}

机构：

[1] Univ Zurich, Inst Math, CH-8057 Zurich, Switzerland

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2013年 / 9卷 / 04期

基金：

瑞士国家科学基金会; 英国工程与自然科学研究理事会;

关键词：

Automorphic L-functions; nonvanishing; mollifier method; two-piece mollifier; DIRICHLET L-FUNCTIONS; HIGH DERIVATIVES; CENTRAL VALUES; ZETA-FUNCTION; ZEROS; RANK;

D O I：

10.1142/S1793042113500115

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the nonvanishing of twists of automorphic L-functions at the center of the critical strip. Given a primitive character chi modulo D satisfying some technical conditions, we prove that the twisted L-functions L(f. chi, s) do not vanish at s = 1/2 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. chi, s), and from that derive an upper bound for the average analytic rank of the studied L-functions.

引用

页码：1015 / 1053

页数：39

共 50 条

[21] BOUNDS FOR AUTOMORPHIC L-FUNCTIONS
DUKE, W
FRIEDLANDER, J
IWANIEC, H
INVENTIONES MATHEMATICAE, 1993, 112 (01) : 1 - 8
[22] L-functions and automorphic representations
Arthur, James
PROCEEDINGS OF THE INTERNATIONAL CONGRESS OF MATHEMATICIANS (ICM 2014), VOL I, 2014, : 171 - 197
[23] Determining L-functions by twists
Kisilevsky, H
JOURNAL OF NUMBER THEORY, 2004, 104 (02) : 287 - 300
[24] On the zeroes of automorphic L-functions
Soulé, C
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1999, 328 (11): : 955 - 958
[25] On the proportion of quadratic character twists of L-functions attached to cusp forms not vanishing at the central point
Kohnen, W
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1999, 508 : 179 - 187
[26] Dirichlet L-functions at the central point
Iwaniec, H
Sarnak, P
NUMBER THEORY IN PROGRESS, VOLS 1 AND 2: VOL 1: DIOPHANTINE PROBLEMS AND POLYNOMIALS; VOL 2: ELEMENTARY AND ANALYTIC NUMBER THEORY;, 1999, : 941 - 952
[27] Fourier coefficients of automorphic L-functions
Kim, Henry H.
INTERNATIONAL JOURNAL OF NUMBER THEORY, 2023, 19 (10) : 2513 - 2521
[28] On the Selberg orthogonality for automorphic L-functions
Muharem Avdispahić
Lejla Smajlović
Archiv der Mathematik, 2010, 94 : 147 - 154
[29] INTEGRAL MOMENTS OF AUTOMORPHIC L-FUNCTIONS
Diaconu, Adrian
Garrett, Paul
JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU, 2009, 8 (02) : 335 - 382
[30] Zero density for automorphic L-functions
Ye, Yangbo
Zhang, Deyu
JOURNAL OF NUMBER THEORY, 2013, 133 (11) : 3877 - 3901

← 1 2 3 4 5 →