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<p>Let <i>d</i>(<i>n</i>) be the number of divisors of <i>n</i>. We investigate the average value of <i>d</i>(<i>a</i><sub><i>f</i></sub>(<i>p</i>))<sup><i>r</i></sup> for <i>r</i> a positive integer and <i>a</i><sub><i>f</i></sub>(<i>p</i>) the <i>p</i>-th Fourier coefficient of a cuspidal eigenform <i>f</i> having integral Fourier coefficients, where <i>p</i> is a prime subject to a constraint on the angle associated with the normalized Fourier coefficient.</p>

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Divisor problems for restricted Fourier coefficients of modular forms

  • 期刊论文

  • 发表日期：

    2026年4月16日

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  • Yuk-Kam Lau,
  • Wonwoong Lee

摘要

Let d(n) be the number of divisors of n. We investigate the average value of d(af(p))r for r a positive integer and af(p) the p-th Fourier coefficient of a cuspidal eigenform f having integral Fourier coefficients, where p is a prime subject to a constraint on the angle associated with the normalized Fourier coefficient.