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arXiv · 2508.17979

The divisor function along arithmetic progressions and binary cubic polynomials

Lasse Grimmelt·Jori Merikoski
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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 $X Y^2+1$.

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Lasse Grimmelt, Jori Merikoski. 2025-08-25. The divisor function along arithmetic progressions and binary cubic polynomials. https://arxiv.org/abs/2508.17979

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