On Fractional Part Sums: A Mean-Square Asymptotics over Short Intervals |
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Authors: | Werner Georg Nowak |
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Affiliation: | Universit?t für Bodenkultur, Wien, Austria, AT
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Abstract: | This article is concerned with sums 𝒮(t) = ∑ n ψ(tf(n/t)) where ψ denotes, essentially, the fractional part minus ?, f is a C 4-function with f″ ≠ 0 throughout, summation being extended over an interval of order t. We establish an asymptotic formula for ∫ T−Λ T+Λ (𝒮(t))2dt for any Λ = Λ(T) growing faster than log T. Received April 30, 2001; in revised form February 15, 2002 RID="a" ID="a" Dedicated to Professor Edmund Hlawka on the occasion of his 85th birthday |
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Keywords: | 2000 Mathematics Subject Classification: 11P21 11K99 |
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