Results 11 to 20 of about 121,729 (283)
Note on the quadratic Gauss sums [PDF]
International Journal of Mathematics and Mathematical Sciences, 2001 Let p be an odd prime and {χ(m)=(m/p)}, m=0,1,...,p−1 be a finite arithmetic sequence with elements the values of a Dirichlet character χ modp which are defined in terms of the Legendre symbol (m/p), (m,p)=1. We study the relation between the Gauss and
George Danas
doaj +2 more sources
Finite Fields and Their Applications, 1998 Let \(m\) be an odd positive integer, \(n\) an arbitrary positive integer, and \(p\) a prime which does not divide \(m\). Let \(\mathbb{F}_{p}\) be a prime finite field, \(\mathbb{F}_{q}\) a finite extension of \(\mathbb{F}_{p}\) of degree \(f\), so \(q=p^{f}\), and \( \chi\) a multiplicative character of \(\mathbb{F}_{q}\) of order \(m\). If \( \zeta_{
Mbodj, Oumar D.
openaire +2 more sources
The hybrid power mean of the quartic Gauss sums and the two-term exponential sums
Advances in Difference Equations, 2018 In this paper, we use the analytic method and the properties of classical Gauss sums to study the computational problems of one kind hybrid power mean of quartic Gauss sums and two-term exponential sums, and give an interesting fourth-order linear ...
Xiaoxue Li
doaj +2 more sources
Evaluations of a Weighted Average of Gauss Sums
Journal of Mathematics, 2021 In this paper, we perform a further investigation for a weighted average of Gauss sums. By making use of some properties of the cotangent function and the Bernoulli polynomials, we explicitly evaluate the weighted average of Gauss sums in terms of the ...
Wen-Kai Shao, Yuan He
doaj +2 more sources
One Kind Special Gauss Sums and their Mean Square Values
Journal of Mathematics, 2021 In this paper, we introduce one kind special Gauss sums; then, using the elementary and analytic methods to study the mean value properties of these kind sums, we obtain several exact calculating formulae for them.
Jianhong Zhao, Jiejie Gao
doaj +2 more sources
Local units and Gauss sums [PDF]
Journal of Number Theory, 2003 Let \(F\) be an abelian number field containing a primitive root of unity \(\zeta _ p\) with Galois group \(\Lambda = {\text{Gal}} (F/{\mathbb Q})\) over \(\mathbb Q\). For a fixed prime number \(p\), let \(F _ \infty\) denote the cyclotomic \({\mathbb Z} _ p\) extension of \(F\), where \({\mathbb Z}_ p\) denotes the ring of \(p\)-adic numbers.
Aoki, Miho
openaire +2 more sources
Some new hybrid power mean formulae of trigonometric sums
Advances in Difference Equations, 2020 We apply the analytic method and the properties of the classical Gauss sums to study the computational problem of a certain hybrid power mean of the trigonometric sums and to prove several new mean value formulae for them.
Li Chen, Zhuoyu Chen
doaj +1 more source
Journal of Mathematics, 2021 In this paper, we use the analytic methods and the properties of the classical Gauss sums to study the properties of the error term of the fourth power mean of the generalized cubic Gauss sums and give two recurrence formulae for it.
Zhang Jin, Zhang Jiafan
doaj +1 more source
Bilinear sums of Gauss sums [PDF]
Acta Arithmetica, 2022 Let \(p \geq 3\) be a prime number. Motivated by results on bilinear sums of Kloosterman sums and their generalisations, the author considers sums with Gauss sums \[ G(m, n)=\sum_{x=1}^{p} \mathbf{e}_{p}\left(m x+n x^{2}\right), \] where \(\mathbf{e}_{p}(z)=\exp (2 \pi i z / p)\).
openaire +2 more sources
A Hybrid Mean Value Involving Dedekind Sums and the Generalized Kloosterman Sums
Journal of Mathematics, 2021 In this paper, we use the mean value theorem of Dirichlet L-functions and the properties of Gauss sums and Dedekind sums to study the hybrid mean value problem involving Dedekind sums and the general Kloosterman sums and give an interesting identity for ...
Xiaowei Pan, Xiaoyan Guo
doaj +1 more source