On triple correlations of Fourier coefficients of cusp forms. II
On triple correlations of Fourier coefficients of cusp forms. II
复制标题
关于尖点形式傅里叶系数的三重相关性。
DOI：
10.1142/s1793042119500374
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发表时间：
2019
影响因子：
0.7
通讯作者：
Xi Ping
中科院分区：
文献类型：
--
作者：
Lü Guangshi;Xi Ping
任意系数[公式：见文]的三重相关性[公式：见文]是在一些短间隔内对[公式：见文]的平均值进行估计。通过引入一个短间隔的装置，我们能够将这个问题简化为三个系数之一的均匀振荡，例如[公式：见文]，相对于[公式：见文]在短间隔内的可加性特征。这个论证很简单，但在某些情况下精炼了前面的论证。将[公式：见文]取为尖点形式和Möbius函数的傅里叶系数，也得到了更精确的估计，这大大改进了以前的结果。
The triple correlation [Formula: see text] for arbitrary coefficients [Formula: see text] is estimated on average over [Formula: see text] in some short intervals. By introducing a device of short intervals, we are able to reduce this problem to uniform oscillations of one of the three coefficients, say [Formula: see text], against additive characters of [Formula: see text] over short intervals. The argument is simple, but refines previous arguments in certain cases. More precise estimates are also obtained by taking [Formula: see text] to be Fourier coefficients of cusp forms and Möbius functions, which substantially improve previous results.