On the distribution of angles of the salié sums

Igor E. Shparlinski*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
30 Downloads (Pure)

Abstract

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.

Original languageEnglish
Pages (from-to)221-227
Number of pages7
JournalBulletin of the Australian Mathematical Society
Volume75
Issue number2
Publication statusPublished - Apr 2007

Bibliographical note

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.

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