Identities of general Kloosterman sums-Reference-Cited by-同舟云学术

Identities of general Kloosterman sums

Published:2023-03-29 Issue:06 Volume:19 Page:1415-1428
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Liu Xiaoge¹^ORCID,Zhang Tianping¹²

Affiliation:

1. School of Mathematics and Statistics, Shaanxi Normal University, Xi’an 710119, Shaanxi, P. R. China

2. Research Center for Number Theory and Its Applications, Northwest University, Xi’an 710127, Shaanxi, P. R. China

Abstract

Let [Formula: see text] be any integers with [Formula: see text], and [Formula: see text] be a Dirichlet character modulo [Formula: see text]. The general Kloosterman sums [Formula: see text] are defined as follows: [Formula: see text] where [Formula: see text], and [Formula: see text] denotes the multiplicative inverse of [Formula: see text] modulo [Formula: see text]. By combining elementary methods and analytic methods, along with Montgomery and Vaughan’s clever trick on primitive characters, we derive some new identities for [Formula: see text] under the condition [Formula: see text], where [Formula: see text] denotes the summation over all [Formula: see text] with [Formula: see text]. Previously only the case of [Formula: see text] was studied.

Funder

National Natural Science Foundation of China

Natural Science Basic Research Plan for Distinguished Young Scholars in Shaanxi Province of China

Publisher

World Scientific Pub Co Pte Ltd

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042123500690

Reference20 articles.

1. On the fourth power mean of the analogous general Kloosterman sum

2. On Kloosterman's sum

3. Power moments of Kloosterman sums

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