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arXiv · 2511.07945

On the exponent of distribution for convolutions of $\mathrm{GL(2)}$ coefficients to smooth moduli

Rongjie Yin
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Abstract

Let $(\lambda_f(n))_{n\geqslant1}$ be the Hecke eigenvalues of a holomorphic cusp form $f$. We prove that the exponent of distribution of $\lambda_f*1$ in arithmetic progressions is as large as $\frac{1}{2}+\frac{1}{46}$ when the modulus $q$ is square-free.

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Rongjie Yin. 2025-11-11. On the exponent of distribution for convolutions of $\mathrm{GL(2)}$ coefficients to smooth moduli. https://arxiv.org/abs/2511.07945

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