Sub-Weyl strength bounds for twisted GL(2) short character sums

2022/09/20 by Ghosh, Aritra, Mallesham, Kummari
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2209.09479

Abstract

Let S(N) = ∑_{n ∼ N}^smooth λ_f(n) χ(n), where λ_f(n)'s are Fourier coefficients of Hecke-eigen form, and χ is a primitive character of conductor p^r. In this article we prove a sub-Weyl strength bounds for S(N). Indeed, we obtain S(N) ≪ N^(5)/(9) p^(13r)/(45), provided that p^13r/20 ≤ N ≤ p^4r/5. Note that the above bound for S(N) is non-trivial if N≥ (p^r)^{(2)/(3)-(1)/(60)}.

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