二元二次方程表示的整数处赫克特征值的第一矩

Manish Kumar Pandey, Lalit Vaishya
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引用次数: 0

摘要

在这篇文章中,我们考虑了一个有关以稀疏整数集为索引的赫克特征形式的傅里叶系数的求和函数估计的问题。其中,"和 "表示遍历无平方正整数,"傅里叶系数 "表示同余子群积分权重赫克特征形式的归一化th傅里叶系数,"二元二次形式 "是具有固定判别式的原始积分正定二元二次形式,其类号为 。因此,我们以相关-函数的导体为单位,确定了由...表示的整数索引的赫克特征值的第一个符号变化的大小。这项工作是对之前成果的改进和推广。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
First moment of Hecke eigenvalues at the integers represented by binary quadratic forms
In the article, we consider a question concerning the estimation of summatory function of the Fourier coefficients of Hecke eigenforms indexed by a sparse set of integers. In particular, we provide an estimate for the following sum; where means that sum runs over the square-free positive integers, denotes the normalised th Fourier coefficients of a Hecke eigenform of integral weight for the congruence subgroup and is a primitive integral positive-definite binary quadratic forms of fixed discriminant with the class number . As a consequence, we determine the size, in terms of conductor of associated -function, for the first sign change of Hecke eigenvalues indexed by the integers which are represented by . This work is an improvement and generalisation of the previous results.
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