短区间内L$ L$ -函数系数的中心极限定理

IF 0.9 3区数学 Q2 MATHEMATICS Bulletin of the London Mathematical Society Pub Date : 2025-01-22 DOI:10.1112/blms.70002

Sun-Kai Leung

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引用次数: 0

摘要

假设广义Lindelöf假设（GLH）、广义Ramanujan猜想的一个弱版本和Rankin-Selberg型部分和估计，我们建立了一个广义L$ L$ -函数在适当长度的短区间内的系数和的正态性。GLH下的新颖性在于度方面。特别地，这推广了Hughes和Rudnick关于薄环空晶格点计数的结果。

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A central limit theorem for coefficients of L $L$ -functions in short intervals

Assuming the generalized Lindelöf hypothesis (GLH), a weak version of the generalized Ramanujan conjecture and a Rankin–Selberg type partial sum estimate, we establish the normality of the sum of coefficients of a general $L$ -function in short intervals of appropriate length. The novelty lies in the degree aspect under GLH. In particular, this generalizes the result of Hughes and Rudnick on lattice point counts in thin annuli.

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