On the distribution of additive twists of the divisor function and Hecke eigenvalues

2021/10/07 by Pandey, Mayank · 1 citation
#11L07 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2110.03202

Abstract

We obtain asymptotics with a power saving error term for ∫₀¹|∑_{n≤ X} d(n)e(nα)|^sdα for s < 2, where d(n) = ∑_{d | n} 1 is the divisor function. We also obtain such asymptotics for ∫₀¹|∑_{n≤ X}λ_f(n)e(nα)|^sdα for all s > 0. Our proof an iterative method with repeated applications of Jutila's variant of the circle method and Voronoi summation.

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