Proofs of conjectures of Chan for d(n)

被引:0
作者
Cui, Su-Ping [1 ]
机构
[1] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Shandong, Peoples R China
基金
中国国家自然科学基金;
关键词
Partial theta function; Mock theta function; Congruence; CONGRUENCES;
D O I
10.1007/s11139-022-00643-8
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, we prove some congruences for the coefficients of a function related to Ramanujan's sixth-order mock theta function phi(q), which was conjectured by Song Heng Chan.
引用
收藏
页码:287 / 294
页数:8
相关论文
共 11 条
[1]   A LOST NOTEBOOK OF RAMANUJAN - COMMENT [J].
AGARWAL, RP .
ADVANCES IN MATHEMATICS, 1984, 53 (03) :291-300
[2]   The number of smallest parts in the partitions of n [J].
Andrews, George E. .
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2008, 624 :133-142
[3]   Proofs of some conjectures of Chan on Appell-Lerch sums [J].
Baruah, Nayandeep Deka ;
Begum, Nilufar Mana .
RAMANUJAN JOURNAL, 2020, 51 (01) :99-115
[4]   Congruences for Ramanujan's φ function [J].
Chan, Song Heng .
ACTA ARITHMETICA, 2012, 153 (02) :161-189
[5]   TWO CONGRUENCES FOR APPELL-LERCH SUMS [J].
Chan, Song Heng ;
Mao, Renrong .
INTERNATIONAL JOURNAL OF NUMBER THEORY, 2012, 8 (01) :111-123
[6]   Arithmetic properties for Appell-Lerch sums [J].
Ding, W. H. ;
Xia, Ernest X. W. .
RAMANUJAN JOURNAL, 2021, 56 (03) :763-783
[7]   Proof of a conjectural congruence of Chan for Appell-Lerch sums [J].
Fan, Yan ;
Wang, Liuquan ;
Xia, Ernest X. W. .
INTERNATIONAL JOURNAL OF NUMBER THEORY, 2021, 17 (04) :1003-1011
[8]  
Fine N.J., 1988, BASIC HYPERGEOMETRIC, V27, DOI DOI 10.1090/SURV/027
[9]  
Gasper G., 2004, Basic Hypergeometric Series, second edition, Encyclopedia of Mathematics and Its Applications 96, V2nd edn
[10]   Generalizations of some conjectures of Chan on congruences for Appell-Lerch sums [J].
Qu, Y. K. ;
Wang, Y. J. ;
Yao, Olivia X. M. .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 460 (01) :232-238