Abstract
This article is concerned with sums 𝒮(t) = ∑n ψ(tf(n/t)) where ψ denotes, essentially, the fractional part minus ½, f is a C4-function with f″ ≠ 0 throughout, summation being extended over an interval of order t. We establish an asymptotic formula for ∫T−ΛT+Λ(𝒮(t))2dt for any Λ = Λ(T) growing faster than log T.
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