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General asymptotic formula of Fourier coefficients of cusp forms over sum of two squares
Journal of Number Theory ( IF 0.6 ) Pub Date : 2021-09-03 , DOI: 10.1016/j.jnt.2021.07.017
Chenran Xu 1
Affiliation  

Let λf(n) denote the nth normalized Fourier coefficient of the primitive holomorphic cusp forms of even integral weight k2 for the full modular group SL(2,Z). For x1, we are interested in the sums nxλf(n) and a2+b2xλf(a2+b2). In this paper, we are able to establish the asymptotic formulae for general cases of the power sum for every positive integer N. The special cases of our results improve previous results.



中文翻译:

尖点形式傅里叶系数在两个平方和上的一般渐近公式

λF(n)表示偶整数权重的原始全纯尖点形式的第n个归一化傅立叶系数ķ2对于完整的模块化组小号大号(2,Z). 为了X1, 我们对总和感兴趣nXλF(n)其他一种2+b2XλF(一种2+b2). 在本文中,我们能够为每个正整数的幂和的一般情况建立渐近公式ñ. 我们结果的特殊情况改进了以前的结果。

更新日期:2021-09-03
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