What question did this study set out to answer?

The research aims to prove several instances of vanishing coefficients in specific arithmetic progressions.

December 11, 2025

On some new infinite q -products and their vanishing coefficients

Key Points

The research aims to prove several instances of vanishing coefficients in specific arithmetic progressions.
Utilized elementary q-series manipulations
Applied the Jacobi triple product identity
Focused on a new class of infinite q-products
Proved that for any positive integer n, vanishing coefficients occur under certain conditions in arithmetic progressions.

Abstract

In this paper, we prove several vanishing coefficients in arithmetic progressions modulo Formula: see text, Formula: see text and Formula: see text by using elementary Formula: see text-series manipulations and the Jacobi triple product identity for a new class of infinite Formula: see text-products, namely Formula: see text where Formula: see text is any positive integer, Formula: see text is prime and Formula: see text, Formula: see text and Formula: see text are integers that are relatively prime to Formula: see text. For instance, we prove that for any positive integer Formula: see text, if Formula: see text where Formula: see text, then Formula: see text for all non-negative integers Formula: see text.

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Cite This Study

Baruah et al. (Thu,) studied this question.

synapsesocial.com/papers/69401b172d562116f28f7484 https://doi.org/https://doi.org/10.1142/s1793042126500429

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