Ramanujan's congruences for the partition function modulo 5, 7, and 11

被引：8

作者：

Berndt, Bruce C. ^{[1
]}

机构：

[1] Univ Illinois, Dept Math, Urbana, IL 61801 USA

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2007年 / 3卷 / 03期

关键词：

partition congruences; Eisenstein series; Ramanujan's lost notebook;

D O I：

10.1142/S1793042107000961

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Using Ramanujan's differential equations for Eisenstein series and an idea from Ramanujan's unpublished manuscript on the partition function p(n) and the tau function t(n), we provide simple proofs of Ramanujan's congruences for p(n) modulo 5, 7, and 11.

引用

页码：349 / 354

页数：6

共 50 条

[1] Extension of Ramanujan's congruences for the partition function modulo powers of 5
Lovejoy, J
Ono, K
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2002, 542 : 123 - 132
[2] Infinite families of congruences modulo 7 for Ramanujan’s general partition function
Nipen Saikia
Jubaraj Chetry
[J]. Annales mathématiques du Québec, 2018, 42 (1) : 127 - 132
[3] Infinite families of congruences modulo 7 for Ramanujan's general partition function
Saikia, Nipen
Chetry, Jubaraj
[J]. ANNALES MATHEMATIQUES DU QUEBEC, 2018, 42 (01): : 127 - 132
[4] Infinite Families of Congruences Modulo 5 for Ramanujan's General Partition Function
Chetry, Jubaraj
Saikia, Nipen
[J]. THAI JOURNAL OF MATHEMATICS, 2022, 20 (04): : 1603 - 1608
[5] A REFINEMENT OF RAMANUJAN'S CONGRUENCES MODULO POWERS OF 7 AND 11
Jameson, Marie
[J]. INTERNATIONAL JOURNAL OF NUMBER THEORY, 2012, 8 (04) : 865 - 879
[6] Congruences modulo powers of 5 for Ramanujan's φ function
Du, Julia Q. D.
Tang, Dazhao
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2024, 537 (01)
[7] Arithmetic properties of Ramanujan's general partition function for modulo 11
Kumar, Belakavadi R. Srivatsa
Narendra, Ramakrishna
Rajanna, Karpenahalli R.
[J]. KUWAIT JOURNAL OF SCIENCE, 2021, 48 (01) : 10 - 13
[8] Infinite families of congruences modulo 5 and 7 for the cubic partition function
Yao, Olivia X. M.
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2019, 149 (05) : 1189 - 1205
[9] RAMANUJAN-TYPE CONGRUENCES MODULO POWERS OF 5 AND 7
Ranganatha, D.
[J]. INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2017, 48 (03): : 449 - 465
[10] Ramanujan-type congruences modulo powers of 5 and 7
D. Ranganatha
[J]. Indian Journal of Pure and Applied Mathematics, 2017, 48 : 449 - 465

← 1 2 3 4 5 →