DISTRIBUTION OF MOMENTS OF HURWITZ CLASS NUMBERS IN ARITHMETIC PROGRESSIONS AND HOLOMORPHIC PROJECTION

被引：3
作者：
Kane, Ben [1 ]
Pujahari, Sudhir [2 ]
机构：
[1] Univ Hong Kong, Dept Math, Pokfulam, Hong Kong, Peoples R China
[2] Homi Bhabha Natl Inst, Natl Inst Sci Educ & Res, Sch Math Sci, Khurja 752050, Orissa, India
来源：
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2023年 / 376卷 / 08期
关键词：
Holomorphic projection; elliptic curves; trace of Frobenius; Hurwitz class numbers; ELLIPTIC-CURVES; FINITE-FIELD; MODULAR-FORMS; POINTS; SUMS;
D O I：
10.1090/tran/8885
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study moments of Hurwitz class numbers associated to imaginary quadratic orders restricted into fixed arithmetic progressions. In particular, we fix t in an arithmetic progression t = m (mod M) and consider the ratio of the 2k-th moment to the zeroeth moment for H(4n - t2) as one varies n. The special case n = pr yields as a consequence asymptotic formulas for moments of the trace t = m (mod M) of Frobenius on elliptic curves over finite fields with pr elements.
引用
收藏
页码：5503 / 5519
页数：17
相关论文
共 47 条
  • [1] Ahmadi O., 2009, ARXIV
  • [2] [Anonymous], 2012, DIGITAL LIB MATH FUN
  • [3] Quadratic bodies in areas of higher conguence. II. (Analytical part)
    Artin, E
    [J]. MATHEMATISCHE ZEITSCHRIFT, 1924, 19 : 207 - 246
  • [4] Barban M. B., 1966, SOV MATH, V7, P356
  • [5] A Family of Calabi-Yau Varieties and Potential Automorphy II
    Barnet-Lamb, Tom
    Geraghty, David
    Harris, Michael
    Taylor, Richard
    [J]. PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 2011, 47 (01) : 29 - 98
  • [6] Bhand Ajit, 2019, HARDY RAMANUJAN J, V42, P17
  • [7] BIRCH BJ, 1968, J LONDON MATH SOC, V43, P57
  • [8] Sums of class numbers and mixed mock modular forms
    Bringmann, Kathrin
    Kane, Ben
    [J]. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2019, 167 (02) : 321 - 333
  • [9] More points than expected on curves over finite field extensions
    Brock, BW
    Granville, A
    [J]. FINITE FIELDS AND THEIR APPLICATIONS, 2001, 7 (01) : 70 - 91
  • [10] Elliptic curves, modular forms, and sums of Hurwitz class numbers
    Brown, Brittany
    Calkin, Neil J.
    Flowers, Timothy B.
    James, Kevin
    Smith, Ethan
    Stout, Amy
    [J]. JOURNAL OF NUMBER THEORY, 2008, 128 (06) : 1847 - 1863
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