Abstract
For a primepand integersaandb, we consider Salié sumswhere χ2(x) is a quadratic character and x¯ is the modular inversion ofx, that is,xx¯≡ 1 (modp). One can naturally associate withSp(a, b) a certain angle θp(a, b) ∈ [0, π]. We show that, for any fixed ε > 0, these angles are uniformly distributed in [0, π] whenaandbrun over arbitrary sets , ℬ ⊆ {0, 1, …,p− 1} such that there are at leastp1+εquadratic residues modulopamong the productsab, where (a, b) ∈ × ℬ.
Publisher
Cambridge University Press (CUP)
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