Periodic sign changes for weakly holomorphic $\eta$-quotients

TL;DR

This paper investigates the sign change behavior of weakly holomorphic modular forms expressed as eta-quotients, providing examples across various weights to understand their sign variation patterns.

Contribution

It introduces a systematic study of sign changes in eta-quotients of different weights, offering new insights into their behavior.

Findings

Sign changes occur in eta-quotients across all weights studied.

Examples of sign patterns are provided for negative, zero, and positive weights.

The paper advances understanding of the oscillatory nature of weakly holomorphic modular forms.

Abstract

In this paper, we study sign changes of weakly holomorphic modular forms which are given as $\eta$-quotients. We give representative examples for forms of negative weight, weight zero, and positive weight.