On a sign-change conjecture of Schlosser and Zhou

TL;DR

This paper investigates the sign changes of Fourier coefficients in Rogers-Ramanujan type q-series products, proving a conjecture about sign variations for modulus 10, advancing understanding of their oscillatory behavior.

Contribution

It proves a conjecture by Schlosser and Zhou regarding sign changes in Fourier coefficients of specific q-series products for modulus 10.

Findings

Confirmed the sign-change conjecture for modulus 10

Identified patterns in Fourier coefficient sign oscillations

Enhanced understanding of Rogers-Ramanujan type series

Abstract

In this paper, we investigate the signs changes of Fourier coefficients of infinite products of $q$-series of Rogers--Ramanujan type. In particular, we prove a conjecture made by Schlosser--Zhou pertaining to such sign changes for products of modulus $10$.