A simple proof of a congruence for a series involving the little q-Jacobi polynomials

2019/02/16 by Atul Dixit, Dixit, Atul · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT) #Primary: 11P81 #Secondary: 05A17

paper · pdf · doi:10.48550/arxiv.1902.06104

openalex publication_date 2019/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a simple and a more explicit proof of a mod 4 congruence for a series involving the little q-Jacobi polynomials which arose in a recent study of a certain restricted overpartition function.

Cited by

• Non-Rascoe partitions and a rank parity function associated to the Rogers-Ramanujan partitions

Related

• Overpartitions related to the mock theta function ω(q)
• Congruences modulo primes of the Romik sequence related to the Taylor expansion of the Jacobi theta constant θ₃
• The congruence properties of Romik's sequence of Taylor coefficients of Jacobi's theta function θ₃
• Simpler congruences for Jacobi sum J(1, 1)₄₉ of order 49
• Some congruences modulo 5 and 25 for overpartition