A family of super congruences involving multiple harmonic sums

被引：4

作者：

Mccoy, Megan ^{[1
]}

Thielen, Kevin ^{[1
]}

Wang, Liuquan ^{[2
]}

Zhao, Jianqiang ^{[3
]}

机构：

[1] Eckerd Coll, Dept Math, St Petersburg, FL 33711 USA

[2] Natl Univ Singapore, Dept Math, Singapore 119076, Singapore

[3] Bishops Sch La Jolla, Dept Math, La Jolla, CA 92037 USA

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2017年 / 13卷 / 01期

关键词：

Multiple harmonic sums; Bernoulli numbers; super congruences; CURIOUS CONGRUENCE; BERNOULLI NUMBERS; MELLIN TRANSFORMS; INTEGRALS;

D O I：

10.1142/S1793042117500075

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In recent years, the congruence Sigma(i+j+k=p) (i, j, k>0) 1/ijk equivalent to -2B(p-3) (mod p), first discovered by the last author has been generalized by either increasing the number of indices and considering the corresponding super congruences, or by considering the alternating version of multiple harmonic sums. In this paper, we prove a family of similar super congruences modulo prime powers p(r) with the indices summing up to mp(r) where m is coprime to p, and where all the indices are also coprime to p.

引用

页码：109 / 128

页数：20

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