The divisor function along arithmetic progressions and binary cubic polynomials
Lasse Grimmelt, Jori Merikoski
公開日: 2025/8/25
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 $X Y^2+1$.