Results 31 to 40 of about 20,647 (117)

The hybrid power mean of the generalized Gauss sums and the generalized two-term exponential sums

AIMS Mathematics
This article applied the properties of character sums, quadratic character, and classical Gauss sums to study the calculations of the hybrid power mean of the generalized Gauss sums and the generalized two-term exponential sums.
Xue Han, Tingting Wang
semanticscholar   +1 more source

On the arithmetic of a family of twisted constant elliptic curves

, 2019
Let $\mathbb{F}_r$ be a finite field of characteristic $p>3$. For any power $q$ of $p$, consider the elliptic curve $E=E_{q,r}$ defined by $y^2=x^3 + t^q -t$ over $K=\mathbb{F}_r(t)$.
Griffon, Richard, Ulmer, Douglas
core   +1 more source

Computing Dirichlet character sums to a power-full modulus

, 2014
The Postnikov character formula is used to express large portions of a Dirichlet character sum in terms of quadratic exponential sums. The quadratic sums are then computed using an analytic algorithm previously derived by the author.
Hiary, Ghaith A.
core   +1 more source

Abstract algebra, projective geometry and time encoding of quantum information

, 2005
Algebraic geometrical concepts are playing an increasing role in quantum applications such as coding, cryptography, tomography and computing. We point out here the prominent role played by Galois fields viewed as cyclotomic extensions of the integers ...
Planat, Michel R. P., Saniga, Metod
core   +4 more sources

Orbital L-functions for the space of binary cubic forms

, 2011
We introduce the notion of orbital L-functions for the space of binary cubic forms and investigate their analytic properties. We study their functional equations and residue formulas in some detail.
Datskovsky, Datskovsky, Delone, Fouvry, Frank Thorne, Gan, Gelbart, Iwaniec, Saito, Shintani, Takashi Taniguchi, Yukie   +11 more
core   +3 more sources

Factorization of numbers with Gauss sums: I. Mathematical background

, 2011
We use the periodicity properties of generalized Gauss sums to factor numbers. Moreover, we derive rules for finding the factors and illustrate this factorization scheme for various examples.
Averbukh, I. Sh., Girard, B., Merkel, W., Schleich, W. P., Wölk, S.   +4 more
core   +3 more sources

Huyghens, Bohr, Riemann and Galois: Phase-Locking

, 2005
Several mathematical views of phase-locking are developed. The classical Huyghens approach is generalized to include all harmonic and subharmonic resonances and is found to be connected to 1/f noise and prime number theory.
Bouchiat V., Dodonov V. V., Dos Santos S., Iwaniec Henryk, Klapper J., Lidl R., Madelung E., MICHEL PLANAT, Planat M.   +8 more
core   +2 more sources

A note on the sign (unit root) ambiguities of Gauss sums in index 2 and 4 cases

, 2009
Recently, the explicit evaluation of Gauss sums in the index 2 and 4 cases have been given in several papers (see [2,3,7,8]). In the course of evaluation, the sigh (or unit root) ambiguities are unavoidably occurred.
B. C. Berndt, C. F. Gauss, J. Yang, J. Yang, Jing Yang, K. Feng, K. Feng, K. Ireland, L. Stickelberger, Lingli Xia, M. V. Vlugt, O. D. Mbodj, P. Langevin, P. Meijer, R. J. McEliece, R. Lidl   +15 more
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Gauss Sums, Stickelberger's Theorem, and the Gras Conjecture for Ray Class Groups [PDF]

, 2015
Let $k$ be a real abelian number field and $p$ an odd prime not dividing $[k:\mathbb{Q}]$. For a natural number $d$, let $E_d$ denote the group of units of $k$ congruent to $1$ modulo $d$, $C_d$ the subgroup of $d$-circular units of $E_d$, and $\mathfrak{
Timothy All
semanticscholar   +1 more source

Character Sums, Gaussian Hypergeometric Series, and a Family of Hyperelliptic Curves

, 2015
We study the character sums \[\phi_{(m,n)}(a,b)=\sum_{x\in\mathbb{F}_q}\phi\left(x(x^{m}+a)(x^{n}+b)\right),\textrm{ and, } \psi_{(m,n)}(a,b)=\sum_{x\in\mathbb{F}_q}\phi\left((x^{m}+a)(x^{n}+b)\right)\] where $\phi$ is the quadratic character defined ...
Sadek, Mohammad
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