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arXiv · 2511.04030

Prime detecting quasi-modular forms in higher level

Ben Kane·Krishnarjun Krishnamoorthy·Yuk-Kam Lau
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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.

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Ben Kane, Krishnarjun Krishnamoorthy, Yuk-Kam Lau. 2025-11-06. Prime detecting quasi-modular forms in higher level. https://arxiv.org/abs/2511.04030

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