TY - JOUR

T1 - On the distribution of angles of the salié sums

AU - Shparlinski, Igor E.

N1 - Copyright 2007 Cambridge University Press. Article originally published in Bulletin of the Australian Mathematical Society, Volume 75, Issue 2, pp. 221-227. The original article can be found at http://dx.doi.org/10.1017/S0004972700039150.

PY - 2007/4

Y1 - 2007/4

N2 - For a prime p and integers a and b, we consider Salié sums S p(a, b) = ∑x=1
p-1χ2(x) exp(2πi(ax + bx̄)/p), where χ2(x) is a quadratic character and x̄ is the modular inversion of x, that is, xx̄ ≡ 1 (mod p). One can naturally associate with Sp(a, b) a certain angle p(a, b) ∈ [0, π]. We show that, for any fixed ε > 0, these angles are uniformly distributed in [0, π] when a and b run over arbitrary setsΑ, Β ⊆ {0,1,...,p -1} such that there are at least p1+ε quadratic residues modulo p among the products ab, where (a, b) ∈ Α× Β. Copyright Clearance Centre, Inc.

AB - For a prime p and integers a and b, we consider Salié sums S p(a, b) = ∑x=1
p-1χ2(x) exp(2πi(ax + bx̄)/p), where χ2(x) is a quadratic character and x̄ is the modular inversion of x, that is, xx̄ ≡ 1 (mod p). One can naturally associate with Sp(a, b) a certain angle p(a, b) ∈ [0, π]. We show that, for any fixed ε > 0, these angles are uniformly distributed in [0, π] when a and b run over arbitrary setsΑ, Β ⊆ {0,1,...,p -1} such that there are at least p1+ε quadratic residues modulo p among the products ab, where (a, b) ∈ Α× Β. Copyright Clearance Centre, Inc.

UR - http://www.scopus.com/inward/record.url?scp=34248347452&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:34248347452

SN - 0004-9727

VL - 75

SP - 221

EP - 227

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

IS - 2

ER -