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A Recursive Formula and an Estimation for a Specific Exponential Sum

A Recursive Formula and an Estimation for a Specific Exponential Sum

Year:    2022

Author:    Xiwang Cao, Liqin Qian

Communications in Mathematical Research , Vol. 38 (2022), Iss. 2 : pp. 184–205

Abstract

Let Fq be a finite field and Fqs be an extension of Fq. Let f(x)Fq[x] be a polynomial of degree n with gcd(n,q)=1. We present a recursive formula for evaluating the exponential sum cFqsχ(s)(f(x)). Let a and b be two elements in Fq with a a0, u be a positive integer. We obtain an estimate for the exponential sum cFqsχ(s)(acu+bc1), where χ(s) is the lifting of an additive character χ of Fq. Some properties of the sequences constructed from these exponential sums are provided too.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cmr.2021-0030

Communications in Mathematical Research , Vol. 38 (2022), Iss. 2 : pp. 184–205

Published online:    2022-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    22

Keywords:    Exponential sums finite fields Dickson polynomials sequences.

Author Details

Xiwang Cao Email

Liqin Qian Email