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arXiv · 2404.04749

The distribution of $d_4(n)$ in arithmetic progressions

Tomos Parry
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Abstract

We use the Petrow-Young [10] subconvexity bound for Dirichlet $L$-functions to show that $d_4(n)$ has exponent of distribution $4/7$ when we allow an average over $a$ mod $q$, thereby giving an equidistribution result for $d_4(n)$ which goes past the $1/2$ barrier for the first time.

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Tomos Parry. 2024-04-06. The distribution of $d_4(n)$ in arithmetic progressions. https://arxiv.org/abs/2404.04749

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