Year: 2025
Type: preprint
Abstract: We prove a new equidistribution estimate for the divisor function in arithmetic progression to moduli that have two small factors. We give two applications. First, we show an asymptotic formula for the divisor function over arithmetic progressions to almost all moduli of exponent $2/3$. Second, we show an asymptotic formula for the divisor function along the nonhomogeneous binary cubic polynomial $X Y^2+1$.
Source: arXiv (Cornell University)
Authors: Grimmelt, Lasse, Merikoski, Jori
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7077856536
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