Sums of algebraic trace functions twisted by arithmetic functions
Sums of algebraic trace functions twisted by arithmetic functions
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DOI：
10.2140/pjm.2020.304.505
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发表时间：
2018-04
影响因子：
0.6
通讯作者：
Maxim Korolev;Igor Shparlinski
中科院分区：
文献类型：
--
作者：
Maxim Korolev;Igor Shparlinski
抽象的。我们获得了与有界导体的某个束模素数 p 相关的同型迹函数短和的新界，并由莫比乌斯函数和广义除数函数扭曲。这些迹函数包括 Kloosterman 和以及其他几个经典数论对象。对于长度至少为 p 且任意固定 ε > 0 的区间，我们的界限是非平凡的，对于莫比乌斯函数来说，它比长度至少 p 短，而对于 É 的最新结果中所需的除数函数来说，它的长度至少比 p 短。 Fouvry、E. Kowalski 和 P. Michel (2014) 以及 E. Kowalski、P. Michel 和 W. Sawin (2018)。
Abstract. We obtain new bounds for short sums of isotypic trace functions associated to some sheaf modulo prime p of bounded conductor, twisted by the Möbius function and also by the generalised divisor function. These trace functions include Kloosterman sums and several other classical number theoretic objects. Our bounds are nontrivial for intervals of length at least p with an arbitrary fixed ε > 0, which is shorter than the length at least p in the case of the Möbius function and at least p in the case of the divisor function required in recent results of É. Fouvry, E. Kowalski and P. Michel (2014) and E. Kowalski, P. Michel and W. Sawin (2018), respectively.