Explicit evaluations of some weil sums

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August undefined, 2024

WebJan 1, 2000 · In this paper, we evaluate two classes of new exponential sums, which are viewed as gener-2 alized Moisio's exponential sums in contrast to the results by Heng … WebExplicit evaluations of some Weil sums - Acta Arithmetica - Tom 83, Numer 3 (1998) - Biblioteka Nauki - Yadda Artykuł - szczegóły Acta Arithmetica 1998 83 3 241-251 …

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WebDec 31, 1997 · These sums are also known as Weil sums. The problem of explicitly evaluating these sums is quite often difficult. Results giving estimates for the absolute … WebMay 1, 2024 · Weil sums are defined by ∑ x ∈ F q χ ( f ( x)) where f ( x) ∈ F q [ X]. In [4], [5], Coulter evaluated some Weil sums given by S u ( a, b) = ∑ x ∈ F q χ ( a x p u + 1 + b x), a ∈ F q ⁎, b ∈ F q. Lemma 3 If m v be odd, then S u ( a, 0) = G ( η) η ( a) = { ( − 1) m − 1 q η ( a), if p ≡ 1 ( mod 4), ( − 1) m − 1 ( − 1) m q η ( a), if p ≡ 3 ( mod 4). batman tas poster

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WebJan 31, 2002 · In the series of works by Coulter [6,7,8] which were based on Carlitz's proof methods [4], they explicitly evaluated the Weil sums of f (x) = ax p α +1 + L (x) over F p n with linearized... WebFeb 14, 2024 · The evaluation of some Weil sums will also help construct more bent functions or planar functions on finite fields. Discover the world's research 20+ … Webis possible to evaluate the Weil sums for any non-trivial additive character simply by manipulating the results obtained using this identity. We denote our Weil sum by S α(a). That is, S α(a) = X x∈F q χ 1(axp α+1). The evaluation splits into two sections: one for … teufel ultima 40 aktiv probleme

Explicit evaluations of some Weil sums - Home ICM

Explicit formulas for Hecke Gauss sums in quadratic number fields

Webexplicit evaluations, character sums, finite field, Weil sum, Carlitz's method Suggest a Subject Subjects You must be logged in to add subjects. Finite fields and commutative … batman tas man batWebIn a recent article [2] the author gave explicit evaluations of all Weil sums with f(X) = aXp +1 and p odd. These were obtained mostly through generalising methods used by Carlitz in [1] who obtained explicit evaluations of Weil sums with f(X) = aXp+1 +bX, p odd. In this article we complete the work begun in [2]. By generalising some teufik mušić

"WebJul 11, 2015 · Here we note that in , the results were obtained by using some facts on quadratic forms and some properties of function fields. In this paper, apart from the techniques in , we use also some explicit evaluations of Weil sums as in [9–11]. In particular, we use explicit evaluations of Weil sums for Eq. in Sect. 3 in the proof of … " - Explicit evaluations of some weil sums

Explicit evaluations of some weil sums

A note on evaluations of some exponential sums - Home ICM

Webwe only explicitly evaluate the Weil sums with ˜ = ˜1 as it is possible to evaluate the Weil sums for any non-trivial additive character simply by manipulating the results obtained … WebFeb 14, 2024 · Evaluation of weil sums for some polynomials and associated quadratic forms February 2024 Authors: Ruikai Chen Université de Vincennes - Paris 8 Sihem Mesnager Université de Vincennes -...

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WebSep 25, 2010 · We derive an explicit formula for Hecke Gauss sums of quadratic number fields. As an immediate consequence we obtain a quadratic reciprocity law in quadrat ... On Jacobi forms, and explicit evaluations of some trigonometric sums. 28 November 2024. ... Evaluation of weil sums for some polynomials and associated quadratic forms. 14 … Webular shape. In all cases, explicit evaluations are obtained. 1. Introduction Let p be a prime and q = pe for some integer e. We denote the finite field of q elements by ¥q and the non-zero elements of Fg by F*. A Weil sum is an exponential sum of the form XlxeF, x(/(x))> where x is a non-trivial additive character of ¥q and / G Fg[X]. In this ...

Web[1] L. Carlitz, Evaluation of some exponential sums over a finite field, Math. Nachr. 96 (1980), 319-339. Zbl0456.12011 [2] R. S. Coulter, Explicit evaluations of some Weil sums, Acta Arith. 83 (1998), 241-251. Zbl0924.11098 [3] R. S. Coulter and R. W. Matthews, Bent polynomials over finite fields, Bull. Austral. Math. Soc. 56 (1997), 429-437. http://matwbn.icm.edu.pl/ksiazki/aa/aa93/aa9322.pdf

WebJan 20, 2009 · In response to a letter from Goldbach, Euler considered sums of the form where s and t are positive integers. As Euler discovered by a process of extrapolation … WebEXPLICIT EVALUATIONS OF SOME WEIL SUMS ROBERT S. COULTER 1. Introduction In this article we will explicitly evaluate exponential sums of the form X x2Fq ˜(axp +1) where ˜ is a non-trivial additive character of the nite eld Fq with q = pe odd and a 2 Fq. The case a = 0 is trivial and so we assume throughout that a 6= 0.

WebOct 1, 2002 · Explicit evaluations of some Weil sums Acta Arith., 83 ( 1998), pp. 241 - 251 CrossRef View Record in Scopus Google Scholar 2 R.S. Coulter Further evaluations of Weil sums Acta Arith., 86 ( 1998), pp. 217 - 226 CrossRef View Record in Scopus Google Scholar 3 R.S. Coulter On the evaluation of a class of Weil sums in characteristic 2

WebDec 1, 2009 · The evaluation of an exponential sum over a finite field is a very hard problem in general, and it has been achieved only in certain special cases (see e.g. … teufik selimović buđoniWebJan 1, 1998 · Explicit evaluations of some Weil sums The University of Queensland's institutional repository, UQ eSpace, aims to create global visibility and accessibility of … batman tas vpxWebJun 25, 2024 · In this note, we extend the definition of multiple harmonic sums and apply their stuffle relations to obtain explicit evaluations of the sums $R_n(p,t)=\sum\nolimits ... batman tas penguinWebWeil sums are exponential sums whose summation runs over the evaluation mapping of a particular function. Explicitly they have the form X x∈Fq χ(f(x)) where Fq denotes the … teufelsquadrat projektmanagementWebCiteSeerX — Explicit evaluations of some Weil sums by CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): sums of the form ∑ x∈Fq χ(axp α+1) … teufel hrvatski prijevodWebDec 1, 2009 · Explicit evaluations of some Weil sums. Article. Jan 1998; Robert S Coulter; where is a non-trivial additive character of the nite eld Fq with q = pe odd and a … batman tas povWebCiteSeerX — Explicit evaluations of some Weil sums by CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): sums of the form ∑ x∈Fq χ(axp α+1) Documents Authors Tables Documents: Advanced SearchInclude Citations Authors: Advanced SearchInclude Citations Tables: DMCA teugi pirozzi