Prime detecting quasi-modular forms in higher level
Number Theory
2026-05-19 v2
Abstract
In a previous work, the authors resolved a conjecture about the structure of prime-detecting quasi-modular forms by studying sign changes occurring in quasi-modular cusp forms. In this paper, we extend the considerations to prime-detecting quasi-modular forms of higher level, in particular describing the structure of the space of quasi-modular forms that detect primes in various arithmetic progressions. We also provide an ``analytic'' proof of the level one case.
Keywords
Cite
@article{arxiv.2511.04030,
title = {Prime detecting quasi-modular forms in higher level},
author = {Ben Kane and Krishnarjun Krishnamoorthy and Yuk-Kam Lau},
journal= {arXiv preprint arXiv:2511.04030},
year = {2026}
}