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arXiv · 1502.07295

On the asymptotic behaviour of the square root of fractional part summatory function and generalization to the n-th root case

Haroun Meghaichi
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Abstract

We provide an asymptotic expansion for $\sum_{k=1}^n \left\{\sqrt{k}\right\}$. In the same spirit, we discuss the case of n-th root and it relation to special values of Riemman's zeta function.

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Haroun Meghaichi. 2015-02-17. On the asymptotic behaviour of the square root of fractional part summatory function and generalization to the n-th root case. https://arxiv.org/abs/1502.07295

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