Arithmetic properties for Appell-Lerch sums

被引：3
作者：
Ding, W. H. [1 ]
Xia, Ernest X. W. [1 ]
机构：
[1] Suzhou Univ Sci & Technol, Sch Math Sci, Suzhou 215009, Jiangsu, Peoples R China
来源：
RAMANUJAN JOURNAL | 2021年 / 56卷 / 03期
基金：
美国国家科学基金会;
关键词：
Appell-Lerch sums; Generalized Lambert series; Congruence; CONGRUENCES; RAMANUJANS;
D O I：
10.1007/s11139-021-00497-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Recently, Chan proved some congruences and gave several conjectures for Appell-Lerch sums. Qu, Wang and Yao proved congruences modulo 2 which generalize some conjectures given by Chan. In this paper, we prove new congruences modulo 4 and 5 for Appell-Lerch sums.
引用
收藏
页码：763 / 783
页数：21
相关论文
共 16 条
  • [1] RAMANUJAN LOST NOTEBOOK .7. THE 6TH ORDER MOCK THETA FUNCTIONS
    ANDREWS, GE
    HICKERSON, D
    [J]. ADVANCES IN MATHEMATICS, 1991, 89 (01) : 60 - 105
  • [2] Appell, 1884, ANN SCI COLE NORM SU, V2, P9, DOI [10.24033/asens.248, DOI 10.24033/ASENS.248]
  • [3] Appell M.P., 1884, Ann. Scient. l'ENS, 3e serie, VI, P9
  • [4] Appell P., 1884, Ann. Sci. c. Norm. Supr, V3, P135, DOI [10.24033/asens.236, DOI 10.24033/ASENS.236]
  • [5] Berndt B.C., 1991, Ramanujan's Notebook, DOI 10.1007/978-1-4612-0965-2
  • [6] Congruences for Ramanujan's φ function
    Chan, Song Heng
    [J]. ACTA ARITHMETICA, 2012, 153 (02) : 161 - 189
  • [7] TWO CONGRUENCES FOR APPELL-LERCH SUMS
    Chan, Song Heng
    Mao, Renrong
    [J]. INTERNATIONAL JOURNAL OF NUMBER THEORY, 2012, 8 (01) : 111 - 123
  • [8] Heeke-type double sums, Appell Lerch sums, and mock theta functions, I
    Hickerson, Dean R.
    Mortenson, Eric T.
    [J]. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2014, 109 : 382 - 422
  • [9] CUBIC ANALOGS OF THE JACOBIAN THETA-FUNCTION THETA(Z,Q)
    HIRSCHHORN, M
    GARVAN, F
    BORWEIN, J
    [J]. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1993, 45 (04): : 673 - 694
  • [10] Hirschhorn M. D., 2005, Journal of Combinatorial Mathematics and Combinatorial Computing, V53, P65
12