Moments and equidistributions of multiplicative analogues of Kloosterman sums
Moments and equidistributions of multiplicative analogues of Kloosterman sums
复制标题
Kloosterman和的乘法模拟的矩与等分布
DOI：
10.4064/aa211223-10-11
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发表时间：
2021-05
期刊：
影响因子：
0.7
通讯作者：
Ping Xi
中科院分区：
文献类型：
--
作者：
Ping Xi
We consider a family of character sums as multiplicative analogues of Kloosterman sums. Using Gauss sums, Jacobi sums and Deligne's bound for hyper-Kloosterman sums, we establish asymptotic formulae for any real (positive) moments of the above character sum as the character runs over all non-trivial multiplicative characters mod $p.$ Moreover, an arcsine law is also established as a consequence of the method of moments. The evaluations of these moments also allow us to obtain asymptotic formulae for moments of such character sums weighted by special $L$-values (at $1/2$ and $1$).
