New congruences modulo 9 for the coefficients of Gordon-McIntosh's mock theta function ξ(q)

被引：1
作者：
Yao, Olivia X. M. [1 ]
机构：
[1] Suzhou Univ Sci & Technol, Sch Math Sci, Suzhou 215009, Jiangsu, Peoples R China
来源：
QUAESTIONES MATHEMATICAE | 2024年 / 47卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Mock theta functions; congruences; sums of squares; theta functions;
D O I：
10.2989/16073606.2023.2205604
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In recent years, congruence properties for the coefficients of mock theta functions have been studied by mathematicians. Recently, Silva and Sellers proved some congruences modulo 3 and 9 for the coefficients of the third order mock theta function xi(q) given by Gordon and McIntosh. Motivated by their work, we prove new congruences modulo 9 for the coefficients of xi(q) based on the formula for the number of representations of an integer as sums of seven squares in this paper. Those congruences involve in_nitely many primes.
引用
收藏
页码：239 / 248
页数：10
相关论文
共 20 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] Andrews GE, 2017, RAMANUJAN J, V43, P347, DOI 10.1007/s11139-016-9812-2
  • [3] Berndt B. C., 1991, RAMANUJANS NOTEBOOKS
  • [4] Sixth order mock theta functions
    Berndt, Bruce C.
    Chan, Song Heng
    [J]. ADVANCES IN MATHEMATICS, 2007, 216 (02) : 771 - 786
  • [5] Congruences related to an eighth order mock theta function of Gordon and McIntosh
    Brietzke, Eduardo H. M.
    da Silva, Robson
    Sellers, James A.
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 479 (01) : 62 - 89
  • [6] Sums of five, seven and nine squares
    Cooper, S
    [J]. RAMANUJAN JOURNAL, 2002, 6 (04) : 469 - 490
  • [7] da Silva R, 2022, RAMANUJAN J, V58, P815, DOI 10.1007/s11139-021-00479-8
  • [8] Modular transformations of Ramanujan's fifth and seventh order mock theta functions
    Gordon, B
    Mcintosh, RJ
    [J]. RAMANUJAN JOURNAL, 2003, 7 (1-3) : 193 - 222
  • [9] Some eighth order mock theta functions
    Gordon, B
    McIntosh, RJ
    [J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2000, 62 : 321 - 335
  • [10] Gordon B., 2012, DEV MATH, V23, P95, DOI [DOI 10.1007/978-1-4614-0028-8, DOI 10.1007/978-1-4614-0028-8_]
12