Sign changes of Fourier coefficients for holomorphic eta-quotients

TL;DR

This paper investigates the sign changes of a broad class of holomorphic eta-quotients, revealing their behavior as modular forms and exploring connections to Hurwitz class numbers.

Contribution

It provides new insights into the sign variation of eta-quotients and establishes a link to Hurwitz class numbers, expanding understanding of their modular properties.

Findings

Identified sign change patterns of eta-quotients.

Established a relation between eta-quotients and Hurwitz class numbers.

Enhanced comprehension of modular form behavior.

Abstract

In this paper we study sign changes of an infinite class of $\eta$-quotients which are holomorphic modular forms. There is also a relation to Hurwitz class numbers.