Quantum modularity of partial theta series with periodic coefficients

被引：6
|
作者：
Goswami, Ankush [2 ]
Osburn, Robert [1 ]
机构：
[1] Univ Coll Dublin, Sch Math & Stat, Dublin 4, Ireland
[2] Johannes Kepler Univ Linz, Res Inst Symbol Computat RISC, A-4040 Linz, Austria
来源：
FORUM MATHEMATICUM | 2021年 / 33卷 / 02期
基金：
奥地利科学基金会;
关键词：
Quantum modular forms; partial theta series; periodic functions; Kontsevich-Zagier series; torus knots; INVARIANTS; FORMS;
D O I：
10.1515/forum-2020-0201
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We explicitly prove the quantum modularity of partial theta series with even or odd periodic coefficients. As an application, we show that the Kontsevich-Zagier series F-t (q) which matches (at a root of unity) the colored Jones polynomial for the family of torus knots T(3, 2(t)), t >= 2, is a weight 3/2 quantum modular form. This generalizes Zagier's result on the quantum modularity for the "strange" series F(q).
引用
收藏
页码：451 / 463
页数：13
相关论文
共 50 条
  • [1] Resurgence and Partial Theta Series
    Han, Li
    Li, Yong
    Sauzin, David
    Sun, Shanzhong
    [J]. FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 2023, 57 (03) : 248 - 265
  • [2] Resurgence and Partial Theta Series
    Li Han
    Yong Li
    David Sauzin
    Shanzhong Sun
    [J]. Functional Analysis and Its Applications, 2023, 57 : 248 - 265
  • [3] FOURIER COEFFICIENTS OF SEXTIC THETA SERIES
    Broeker, Reinier
    Hoffstein, Jeff
    [J]. MATHEMATICS OF COMPUTATION, 2016, 85 (300) : 1901 - 1927
  • [4] Knots, Perturbative Series and Quantum Modularity
    Garoufalidis, Stavros
    Zagier, Don
    [J]. SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2024, 20
  • [5] Dirichlet series with periodic coefficients
    Ishibashi M.
    Kanemitsu S.
    [J]. Results in Mathematics, 1999, 35 (1-2) : 70 - 88
  • [6] On Dirichlet series with periodic coefficients
    Steuding, J
    [J]. RAMANUJAN JOURNAL, 2002, 6 (03): : 295 - 306
  • [7] Dirichlet series with periodic coefficients
    Schnee, W.
    [J]. VALUE-DISTRIBUTIONS OF L-FUNCTIONS, 2007, 1877 : 209 - 227
  • [8] On Dirichlet Series with Periodic Coefficients
    Jörn Steuding
    [J]. The Ramanujan Journal, 2002, 6 : 295 - 306
  • [9] ON THE FOURIER COEFFICIENTS OF BIQUADRATIC THETA-SERIES
    ECKHARDT, C
    PATTERSON, SJ
    [J]. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1992, 64 : 225 - 264
  • [10] SOME RESULTS ON THE COEFFICIENTS OF THE BIQUADRATIC THETA SERIES
    SUZUKI, T
    [J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1983, 340 : 70 - 117
12345