A Zero Density Estimate for Dedekind Zeta Functions

被引:5
|
作者
Thorner, Jesse [1 ]
Zaman, Asif [2 ]
机构
[1] Univ Illinois, Dept Math, Urbana, IL 61801 USA
[2] Univ Toronto, Dept Math, Toronto, ON M5S 2E4, Canada
基金
加拿大自然科学与工程研究理事会;
关键词
REGION;
D O I
10.1093/imrn/rnac015
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Given a nontrivial finite group G, we prove the first zero density estimate for families of Dedekind zeta functions associated to Galois extensions K/Q with Gal(K/Q) congruent to G that does not rely on unproven progress towards the strong form of Artin's conjecture. We use this to remove the hypothesis of the strong Artin conjecture from the work of Pierce, Turnage-Butterbaugh, and Wood on the average error in the Chebotarev density theorem and l-torsion in ideal class groups.
引用
收藏
页码:6739 / 6761
页数:23
相关论文
共 50 条
  • [1] Explicit zero density theorems for Dedekind zeta functions
    Kadiri, Habiba
    Ng, Nathan
    JOURNAL OF NUMBER THEORY, 2012, 132 (04) : 748 - 775
  • [2] Zeta Functions for the Adjoint Action of GL(n) and Density of Residues of Dedekind Zeta Functions
    Matz, Jasmin
    FAMILIES OF AUTOMORPHIC FORMS AND THE TRACE FORMULA, 2016, : 351 - 433
  • [3] EXPLICIT ZERO-FREE REGIONS FOR DEDEKIND ZETA FUNCTIONS
    Kadiri, Habiba
    INTERNATIONAL JOURNAL OF NUMBER THEORY, 2012, 8 (01) : 125 - 147
  • [4] Dedekind zeta-functions and Dedekind sums
    Lu, HW
    Jiao, RZ
    Ji, CG
    SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY, 2002, 45 (08): : 1059 - 1065
  • [5] Dedekind zeta-functions and Dedekind sums
    Hongwen Lu
    Rongzheng Jiao
    Chungang Ji
    Science in China Series A: Mathematics, 2002, 45 : 1059 - 1065
  • [6] Dedekind zeta-functions and Dedekind sums
    陆洪文
    焦荣政
    纪春岗
    Science China Mathematics, 2002, (08) : 1059 - 1065
  • [7] Multiple Dedekind zeta functions
    Horozov, Ivan Emilov
    JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2017, 722 : 65 - 104
  • [8] ON THE LOWEST ZERO OF THE DEDEKIND ZETA FUNCTION
    Kala, Sushant
    BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2024,
  • [9] On the Northcott property of Dedekind zeta functions
    Genereux, Xavier
    Lalin, Matilde
    RAMANUJAN JOURNAL, 2024, 64 (01): : 67 - 78
  • [10] On the Northcott property of Dedekind zeta functions
    Xavier Généreux
    Matilde Lalín
    The Ramanujan Journal, 2024, 63 : 1135 - 1178