TY - JOUR

T1 - The distribution of values of short hybrid exponential sums on curves over finite fields

AU - Mak, Kit Ho

AU - Zaharescu, Alexandru

N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2011/1

Y1 - 2011/1

N2 - Let p be a prime number, X be an absolutely irreducible affine plane curve over Fp, and g, f ε Fp(x, y). We study the distribution of the values of the hybrid exponential sums sn = σ PiεX, ni)≤n+H y(Pi)ε J X(g(Pi)) ψ(f(Pi)) on n ε I for some short interval I. We show that under some natural conditions the limiting distribution of the projections of the sum Sn, n ε I on any straight line through the origin is Gaussian as p tends to infinity.

AB - Let p be a prime number, X be an absolutely irreducible affine plane curve over Fp, and g, f ε Fp(x, y). We study the distribution of the values of the hybrid exponential sums sn = σ PiεX, ni)≤n+H y(Pi)ε J X(g(Pi)) ψ(f(Pi)) on n ε I for some short interval I. We show that under some natural conditions the limiting distribution of the projections of the sum Sn, n ε I on any straight line through the origin is Gaussian as p tends to infinity.

KW - Exponential sums

KW - Gaussian distribution

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U2 - 10.4310/MRL.2011.v18.n1.a12

DO - 10.4310/MRL.2011.v18.n1.a12

M3 - Article

AN - SCOPUS:79952136865

VL - 18

SP - 155

EP - 174

JO - Mathematical Research Letters

JF - Mathematical Research Letters

SN - 1073-2780

IS - 1

ER -