$N$-tuple sum analogues for Ramanujan-type congruences

TL;DR

This paper establishes supercongruence relations for truncated N-tuple sums of basic hypergeometric series and provides multiple sum analogs of Ramanujan-type supercongruences, advancing understanding of hypergeometric series in number theory.

Contribution

It introduces new supercongruence relations for N-tuple sums and extends Ramanujan-type supercongruences to double, triple, and quadruple sum cases.

Findings

Proved supercongruence relations for truncated N-tuple sums.

Derived analogs of Ramanujan-type supercongruences for multiple sums.

Enhanced understanding of hypergeometric series in modular arithmetic.

Abstract

In this paper, we prove supercongruence relations for truncated $N$-tuple sums of basic hypergeometric series. As an application, we give double, triple, and quadruple sum analogs of some Ramanujan-type supercongruences.