The divisor function along arithmetic progressions and binary cubic polynomials

2025/08/25 by Grimmelt, Lasse, Merikoski, Jori
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2508.17979

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 Y²+1.

Citations

• Divisor problem in arithmetic progressions modulo a prime power
• The divisor function in arithmetic progressions to smooth moduli

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• Divisor problem in arithmetic progressions modulo a prime power
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• The divisor problem for binary cubic forms