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<p>Motivated by weighted partitions of <i>n</i> that vanish if and only if <i>n</i> is a prime, Craig, van Ittersum, and Ono conjectured a classification of quasimodular forms which detect primes in the sense that the <i>n</i>-th Fourier coefficient vanishes if and only if <i>n</i> is a prime. In this paper, we prove this conjecture by showing that Fourier coefficients of quasimodular cusp forms exhibit infinitely many sign changes.</p>

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On a conjecture about prime-detecting quasimodular forms

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月25日

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  • Ben Kane,
  • Krishnarjun Krishnamoorthy,
  • Yuk-Kam Lau

摘要

Motivated by weighted partitions of n that vanish if and only if n is a prime, Craig, van Ittersum, and Ono conjectured a classification of quasimodular forms which detect primes in the sense that the n-th Fourier coefficient vanishes if and only if n is a prime. In this paper, we prove this conjecture by showing that Fourier coefficients of quasimodular cusp forms exhibit infinitely many sign changes.