The fourth moment of quadratic Dirichlet L-functions over function fields

被引：33
|
作者：
Florea, Alexandra [1 ]
机构：
[1] Stanford Univ, Dept Math, Stanford, CA 94305 USA
来源：
GEOMETRIC AND FUNCTIONAL ANALYSIS | 2017年 / 27卷 / 03期
关键词：
RANDOM-MATRIX THEORY; ZETA-FUNCTIONS; HYPERELLIPTIC CURVES; INTEGRAL MOMENTS; MEAN-VALUE; ZEROS;
D O I：
10.1007/s00039-017-0409-8
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We obtain an asymptotic formula for the fourth moment of quadratic Dirichlet L-functions over , as the base field is fixed and the genus of the family goes to infinity. According to conjectures of Andrade and Keating, we expect the fourth moment to be asymptotic to up to an error of size , where P is a polynomial of degree 10 with explicit coefficients. We prove an asymptotic formula with the leading three terms, which agrees with the conjectured result.
引用
收藏
页码：541 / 595
页数：55
相关论文
共 50 条
  • [41] The eighth moment of Dirichlet L-functions
    Chandee, Vorrapan
    Li, Xiannan
    ADVANCES IN MATHEMATICS, 2014, 259 : 339 - 375
  • [42] ON ZETA AND L-FUNCTIONS OVER QUADRATIC NUMBER FIELDS
    Kokluce, Bulent
    SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES-SIGMA MUHENDISLIK VE FEN BILIMLERI DERGISI, 2008, 26 (04): : 267 - 280
  • [43] Type-I contributions to the one and two level densities of quadratic Dirichlet L-functions over function fields
    Bui, Hung M.
    Florea, Alexandra
    Keating, Jonathan P.
    JOURNAL OF NUMBER THEORY, 2021, 221 : 389 - 423
  • [44] ON EVALUATION OF L-FUNCTIONS OVER REAL QUADRATIC FIELDS
    OKAZAKI, R
    JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, 1991, 31 (04): : 1125 - 1153
  • [45] Moments of quadratic twists of elliptic curve L-functions over function fields
    Bui, Hung M.
    Florea, Alexandra
    Keating, Jonathan P.
    Roditty-Gershon, Edva
    ALGEBRA & NUMBER THEORY, 2020, 14 (07) : 1853 - 1893
  • [46] Motohashi's formula for the fourth moment of individual Dirichlet L-functions and applications
    Kaneko, Ikuya
    FORUM OF MATHEMATICS SIGMA, 2022, 10
  • [47] Twisted first moment of central values of primitive quadratic Dirichlet L-functions
    Gao, Peng
    Zhao, Liangyi
    ACTA ARITHMETICA, 2025,
  • [48] One-level density of zeros of Dirichlet L-functions over function fields
    Lin, Hua
    JOURNAL OF NUMBER THEORY, 2024, 258 : 368 - 413
  • [49] SIEGEL'S MASS FORMULA AND AVERAGES OF DIRICHLET L-FUNCTIONS OVER FUNCTION FIELDS
    Maciak, Piotr
    Morales, Jorge
    ENSEIGNEMENT MATHEMATIQUE, 2011, 57 (3-4): : 393 - 422
  • [50] Global L-functions over function fields
    Gebhard Böckle
    Mathematische Annalen, 2002, 323 : 737 - 795
12345