Cancellation in sums over special sequences on \mathbf\rmGL_m and their applications

2024/11/11 by Qiang Ma, Rui Zhang, Ma, Qiang +1
Computer Science · #11F66 #11L07 #11P55 #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2411.06978

openalex publication_date 2024/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let a(n) be the n-th Dirichlet coefficient of the automorphic L-function or the Rankin--Selberg L-function. We investigate the cancellation of a(n) over sequences linked to the Waring--Goldbach problem, by establishing a nontrivial bound for the additive twisted sums over primes on GL_m . The bound does not depend on the generalized Ramanujan conjecture or the nonexistence of Landau--Siegel zeros. Furthermore, we present an application associated with the Sato--Tate conjecture and propose a conjecture about the Goldbach conjecture on average bound.

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