Supercongruences Involving Multiple Harmonic Sums and Bernoulli Numbers
Kevin Chen and Jianqiang Zhao
Department of Mathematics
The Bishop's School
La Jolla, CA 92037
In this paper, we study some supercongruences involving multiple
harmonic sums by using Bernoulli numbers. Our main theorem generalizes
previous results by many different authors and confirms a conjecture by
the authors and their collaborators. In the proof, we will need not
only the ordinary multiple harmonic sums in which the indices are
ordered, but also some variant forms in which the indices can be
unordered or partially ordered. It is a crucial fact that the unordered
multiple harmonic sums often behave better than the corresponding
ordered sums when one considers congruences. We believe these unordered
sums will play important roles in other studies in the future.
Full version: pdf,
(Concerned with sequences
Received March 15 2017; revised versions received March 26 2017; June 26 2017.
Published in Journal of Integer Sequences, July 1 2017.
Journal of Integer Sequences home page