素数模的扭曲二次特征矩的界
Bounds for moments of twisted quadratic characters of prime modulus
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中文总结 AI 辅助
在广义黎曼假设下，研究素数模扭曲二次特征的傅里叶系数和的矩，确定了未平滑m阶矩的正确量级，得到平滑m阶矩的最优上界并匹配偶数m的下界。
中文摘要 AI 辅助
我们在广义黎曼假设（GRH）下，研究由二次特征χ₈ₚ扭曲的固定全纯Hecke本征形式的傅里叶系数之和的矩，其中p取奇素数。我们对所有实数m≥4，确定了未平滑m阶矩的正确量级；对所有整数m≥4，得到了平滑m阶矩的尖锐上界，其量级为XY^{m/2}(log X)^{m(m-3)/2}；对所有偶数m≥4，匹配的下界表明该界是最优的。
英文摘要
We study, under the Generalized Riemann Hypothesis (GRH), the moments of sums of Fourier coefficients of a fixed holomorphic Hecke eigenform twisted by the quadratic character $χ_{8p}$, where $p$ ranges over odd primes. We establish the correct order of magnitude for the unsmoothed $m$-th moment for all real $m\geq 4$, and a sharp upper bound of order $XY^{m/2}\,\, (\log X)^{m(m-3)/2}\,\,$ for the smoothed $m$-th moment for all integers $m\geq 4$. A matching lower bound for all even integers $m\geq 4$ shows that this bound is optimal.
