Gauss Sums, Jacobi Sums, and Relative Gauss Sums

2020 ◽  
pp. 49-75
Keyword(s):  
Gauss Sums ◽  
Jacobi Sums

scholarly journals Gauss Sums, Jacobi Sums, and p-Ranks of Cyclic Difference Sets

1999 ◽  
Vol 87 (1) ◽  
pp. 74-119 ◽  
Author(s):  
Ronald Evans ◽  
Henk D.L. Hollmann ◽  
Christian Krattenthaler ◽  
Qing Xiang
Keyword(s):  
Difference Sets ◽  
Gauss Sums ◽  
Cyclic Difference Sets ◽  
Jacobi Sums

scholarly journals Evaluating prime power Gauss and Jacobi sums

2017 ◽  
Vol 48 (3) ◽  
pp. 227-240 ◽  
Author(s):  
Misty Ostergaard ◽  
Vincent Pigno ◽  
Christopher Pinner
Keyword(s):  
Prime Power ◽  
Gauss Sums ◽  
Jacobi Sums ◽  
Jacobi Sum ◽  
Simple Evaluation ◽  
Gauss And Jacobi Sums ◽  
Mod P

We show that for any mod $p^m$ characters, $\chi_1, \dots, \chi_k,$ with at least one $\chi_i$ primitive mod $p^m$, the Jacobi sum, $$ \mathop{\sum_{x_1=1}^{p^m}\dots \sum_{x_k=1}^{p^m}}_{x_1+\dots+x_k\equiv B \text{ mod } p^m}\chi_1(x_1)\cdots \chi_k(x_k), $$ has a simple evaluation when $m$ is sufficiently large (for $m\geq 2$ if $p\nmid B$). As part of the proof we give a simple evaluation of the mod $p^m$ Gauss sums when $m\geq 2$ that differs slightly from existing evaluations when $p=2$.

The Gauss sums and Jacobi sums over Galois ring GR(p 2, r)

2013 ◽  
Vol 56 (7) ◽  
pp. 1457-1465 ◽  
Author(s):  
Jin Li ◽  
ShiXin Zhu ◽  
KeQin Feng
Keyword(s):  
Gauss Sums ◽  
Galois Ring ◽  
Jacobi Sums

scholarly journals The Mean Values of Character Sums and Their Applications

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 318
Author(s):  
Jiafan Zhang ◽  
Yuanyuan Meng
Keyword(s):  
Character Sums ◽  
Gauss Sums ◽  
Mean Values ◽  
Special Polynomials ◽  
Elementary Methods ◽  
The Mean

In this paper, we use the elementary methods and properties of classical Gauss sums to study the calculation problems of some mean values of character sums of special polynomials, and obtained several interesting calculation formulae for them. As an application, we give a criterion for determining that 2 is the cubic residue for any odd prime p.

scholarly journals A note on two-term exponential sum and the reciprocal of the quartic Gauss sums

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Wenpeng Zhang ◽  
Xingxing Lv
Keyword(s):  
Exponential Sums ◽  
Exponential Sum ◽  
Gauss Sums ◽  
Power Mean ◽  
Hybrid Power ◽  
Analytic Methods ◽  
Hybrid Power Mean

AbstractThe main purpose of this article is by using the properties of the fourth character modulo a prime p and the analytic methods to study the calculating problem of a certain hybrid power mean involving the two-term exponential sums and the reciprocal of quartic Gauss sums, and to give some interesting calculating formulae of them.

scholarly journals Elliptic Gauss sums and applications to point counting

2010 ◽  
Vol 45 (8) ◽  
pp. 825-836 ◽  
Author(s):  
Preda Mihăilescu ◽  
Victor Vuletescu
Keyword(s):  
Gauss Sums ◽  
Point Counting
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