Exact evaluation of second moments associated with some families of curves over a finite field

Ravi Donepudi; Junxian Li; Alexandru Zaharescu

doi:10.1016/j.ffa.2017.08.005

Exact evaluation of second moments associated with some families of curves over a finite field

Ravi Donepudi
, Junxian Li
, Alexandru Zaharescu

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let F_q be the finite field with q elements. Given an N-tuple Q∈F_q^N, we associate with it an affine plane curve C_Q over F_q. We consider the distribution of the quantity q−#C_q,Q where #C_q,Q denotes the number of F_q-points of the affine curve C_Q, for families of curves parameterized by Q. Exact formulae for first and second moments are obtained in several cases when Q varies over a subset of F_q^N. Families of Fermat type curves, Hasse–Davenport curves and Artin–Schreier curves are also considered and results are obtained when Q varies along a straight line.

Original language	English (US)
Pages (from-to)	331-355
Number of pages	25
Journal	Finite Fields and their Applications
Volume	48
DOIs	https://doi.org/10.1016/j.ffa.2017.08.005
State	Published - Nov 2017

Keywords

Curves over finite fields
Exact formulae
Exponential sums
Families of polynomials

ASJC Scopus subject areas

Theoretical Computer Science
Algebra and Number Theory
General Engineering
Applied Mathematics

Online availability

10.1016/j.ffa.2017.08.005

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title = "Exact evaluation of second moments associated with some families of curves over a finite field",

abstract = "Let Fq be the finite field with q elements. Given an N-tuple Q∈FqN, we associate with it an affine plane curve CQ over Fq. We consider the distribution of the quantity q−\#Cq,Q where \#Cq,Q denotes the number of Fq-points of the affine curve CQ, for families of curves parameterized by Q. Exact formulae for first and second moments are obtained in several cases when Q varies over a subset of FqN. Families of Fermat type curves, Hasse–Davenport curves and Artin–Schreier curves are also considered and results are obtained when Q varies along a straight line.",

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author = "Ravi Donepudi and Junxian Li and Alexandru Zaharescu",

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year = "2017",

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language = "English (US)",

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T1 - Exact evaluation of second moments associated with some families of curves over a finite field

AU - Donepudi, Ravi

AU - Li, Junxian

AU - Zaharescu, Alexandru

PY - 2017/11

Y1 - 2017/11

N2 - Let Fq be the finite field with q elements. Given an N-tuple Q∈FqN, we associate with it an affine plane curve CQ over Fq. We consider the distribution of the quantity q−#Cq,Q where #Cq,Q denotes the number of Fq-points of the affine curve CQ, for families of curves parameterized by Q. Exact formulae for first and second moments are obtained in several cases when Q varies over a subset of FqN. Families of Fermat type curves, Hasse–Davenport curves and Artin–Schreier curves are also considered and results are obtained when Q varies along a straight line.

AB - Let Fq be the finite field with q elements. Given an N-tuple Q∈FqN, we associate with it an affine plane curve CQ over Fq. We consider the distribution of the quantity q−#Cq,Q where #Cq,Q denotes the number of Fq-points of the affine curve CQ, for families of curves parameterized by Q. Exact formulae for first and second moments are obtained in several cases when Q varies over a subset of FqN. Families of Fermat type curves, Hasse–Davenport curves and Artin–Schreier curves are also considered and results are obtained when Q varies along a straight line.

KW - Curves over finite fields

KW - Exact formulae

KW - Exponential sums

KW - Families of polynomials

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UR - https://www.scopus.com/pages/publications/85028691818#tab=citedBy

U2 - 10.1016/j.ffa.2017.08.005

DO - 10.1016/j.ffa.2017.08.005

M3 - Article

AN - SCOPUS:85028691818

SN - 1071-5797

VL - 48

SP - 331

EP - 355

JO - Finite Fields and their Applications

JF - Finite Fields and their Applications

ER -

Exact evaluation of second moments associated with some families of curves over a finite field

Abstract

Keywords

ASJC Scopus subject areas

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