Zero-free regions for spectral averages of Hecke L-functions

被引：1

作者：

Ganguly, Satadal ^{[1
]}

Sandeep, E. M. ^{[2
]}

机构：

[1] Indian Stat Inst, 203 B T Rd, Kolkata 700108, West Bengal, India

[2] Indian Stat Inst, North East Ctr, Solmara PO, Tezpur 784501, Assam, India

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2023年 / 19卷 / 09期

关键词：

Hecke L-functions; non-vanishing; critical strip; integral weight;

D O I：

10.1142/S1793042123501051

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain an explicit zero-free region for a weighted sum of L-functions over the orthogonal basis of Hecke eigen cusp forms of a large integral weight for the full modular group. We also estimate the number of such forms whose L value does not vanish at a given point inside this zero-free region.

引用

页码：2151 / 2162

页数：12

共 50 条

[1] Some explicit zero-free regions for Hecke L-functions
Ahn, Jeoung-Hwan
Kwon, Soun-Hi
[J]. JOURNAL OF NUMBER THEORY, 2014, 145 : 433 - 473
[2] A ZERO-FREE REGION FOR THE HECKE L-FUNCTIONS
COLEMAN, MD
[J]. MATHEMATIKA, 1990, 37 (74) : 287 - 304
[3] Zero free region for spectral averages of Hecke-Maass L-functions
Sandeep, E. M.
[J]. ACTA MATHEMATICA HUNGARICA, 2024, 173 (01) : 253 - 285
[4] Zero-free regions for Dirichlet L-functions
Li, HZ
[J]. QUARTERLY JOURNAL OF MATHEMATICS, 1999, 50 (197): : 13 - 23
[5] EXPLICIT ZERO-FREE REGIONS FOR DIRICHLET L-FUNCTIONS
Kadiri, Habiba
[J]. MATHEMATIKA, 2018, 64 (02) : 445 - 474
[6] EXPLICIT ZERO-FREE REGIONS FOR DIRICHLET L-FUNCTIONS
MCCURLEY, KS
[J]. JOURNAL OF NUMBER THEORY, 1984, 19 (01) : 7 - 32
[7] On the asymptotic criterion for the zero-free regions of certain L-functions
Odzak, Almasa
[J]. TURKISH JOURNAL OF MATHEMATICS, 2016, 40 (03) : 688 - 702
[8] Li's criterion and zero-free regions of L-functions
Brown, FCS
[J]. JOURNAL OF NUMBER THEORY, 2005, 111 (01) : 1 - 32
[9] Applications of zero-free regions on averages and shifted convolution sums of Hecke eigenvalues
Kim, Jiseong
[J]. INTERNATIONAL JOURNAL OF NUMBER THEORY, 2024, 20 (06) : 1565 - 1589
[10] ZERO-FREE REGION OF DIRICHLET L-FUNCTIONS
MOTOHASHI, Y
[J]. PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1978, 54 (10) : 332 - 334

← 1 2 3 4 5 →