顶点形式系数的高阶矩估计，超过两平方和系数的高阶矩估计，超过两平方和系数的高阶矩估计

Pub Date : 2024-04-01 DOI:10.59277/mrar.2024.26.76.1.71

Guodong Hua

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引用次数: 0

摘要

设 f 和 g 分别是全模态群 Γ = SL(2, Z) 的偶数积分权重 k1 和 k2 的两个不同的原始全形尖顶形式。用 λf (n) 和 λg(n) 分别表示 f 和 g 的 n 次归一化傅里叶系数。在本文中，我们考虑求和函数 Xn=a2+b2≤xλf (n)iλg(n)j ，对于 x ≥ 2，其中 a、b∈ Z，i、j ≥ 1 为正整数。

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ESTIMATE FOR HIGHER MOMENTS OF CUSP FORM COEFFICIENTS OVER SUM OF TWO SQUARES COEFFICIENTS OVER SUM OF TWO SQUARES

Let f and g be two distinct primitive holomorphic cusp forms of even integral weights k1 and k2 for the full modular group Γ = SL(2, Z), respectively. Denote by λf (n) and λg(n) the nth normalized Fourier coefficients of f and g, respectively. In this paper, we consider the summatory function X n=a2+b2≤x λf (n)iλg(n)j , for x ≥ 2, where a, b ∈ Z and i, j ≥ 1 are positive integers.

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