LOW-LYING ZEROS OF L-FUNCTIONS FOR MAASS FORMS OVER IMAGINARY QUADRATIC FIELDS

被引：4

作者：

Liu, Sheng-Chi ^{[1
]}

Qi, Zhi ^{[2
]}

机构：

[1] Washington State Univ, Dept Math & Stat, Pullman, WA 99164 USA

[2] Zhejiang Univ, Sch Math Sci, Hangzhou 310027, Peoples R China

来源：

MATHEMATIKA | 2020年 / 66卷 / 03期

关键词：

11M50; (primary); FAMILIES; GL(3);

D O I：

10.1112/mtk.12041

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the 1- or 2-level density of families of L-functions for Hecke-Maass forms over an imaginary quadratic field F. For test functions whose Fourier transform is supported in (-<mml:mfrac>32</mml:mfrac>,<mml:mfrac>32</mml:mfrac>), we prove that the 1-level density for Hecke-Maass forms over F of square-free level q, as N(q) tends to infinity, agrees with that of the orthogonal random matrix ensembles. For Hecke-Maass forms over F of full level, we prove similar statements for the 1- and 2-level densities, as the Laplace eigenvalues tend to infinity.

引用

页码：777 / 805

页数：29

共 50 条

[31] Low-lying Zeros of Quadratic Dirichlet L-Functions, Hyper-elliptic Curves and Random Matrix Theory
Alexei Entin
Edva Roditty-Gershon
Zeév Rudnick
Geometric and Functional Analysis, 2013, 23 : 1230 - 1261
[32] Statistics for low-lying zeros of symmetric power L-functions in the level aspect
Ricotta, Guillaume
Royer, Emmanuel
FORUM MATHEMATICUM, 2011, 23 (05) : 969 - 1028
[33] LOW LYING ZEROS OF FAMILIES OF L-FUNCTIONS
Iwaniec, Henryk
Luo, Wenzhi
Sarnak, Peter
PUBLICATIONS MATHEMATIQUES DE L IHES, 2000, (91): : 55 - 131
[34] Low lying zeros of families of L-functions
Henryk Iwaniec
Wenzhi Luo
Peter Sarnak
Publications Mathématiques de l'Institut des Hautes Études Scientifiques, 2000, 91 (1): : 55 - 131
[35] Low-lying zeros of elliptic curve L-functions: Beyond the Ratios Conjecture
Fiorilli, Daniel
Parks, James
Sodergren, Anders
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2016, 160 (02) : 315 - 351
[36] SIMPLE ZEROS OF MAASS L-FUNCTIONS
Cho, Peter Jaehyun
INTERNATIONAL JOURNAL OF NUMBER THEORY, 2013, 9 (01) : 167 - 178
[37] Zeros of a special type of function associated with Hecke L-functions of imaginary quadratic fields
Gritsenko, SA
IZVESTIYA MATHEMATICS, 1997, 61 (01) : 45 - 68
[38] On the distribution of the nontrivial zeros of quadratic L-functions of imaginary quadratic number fields close to the real axis
Ozluk, A. E.
Snyder, C.
ACTA ARITHMETICA, 2006, 124 (03) : 205 - 233
[39] Sato-Tate theorem for families and low-lying zeros of automorphic L-functions
Shin, Sug Woo
Templier, Nicolas
INVENTIONES MATHEMATICAE, 2016, 203 (01) : 1 - 177
[40] n-level density of the low-lying zeros of primitive Dirichlet L-functions
Chandee, Vorrapan
Lee, Yoonbok
ADVANCES IN MATHEMATICS, 2020, 369

← 1 2 3 4 5 →