A note on the exponential sums of the localized divisor functions

Giovanni Coppola; Maurizio Laporta

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arXiv · 1512.01128

A note on the exponential sums of the localized divisor functions

Giovanni Coppola·Maurizio Laporta

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Abstract

We prove an upper bound for the exponential sum associated to a localized $k-$divisor function, i.e., the counting function of the number of ways to write a positive integer $n$ as a product of $k\ge 2$ positive integers, each of them belonging to a specified interval. In particular, this gives an estimate for the exponential sum for the $k-$divisor function, $d_k(n)$.

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Giovanni Coppola, Maurizio Laporta. 2015-12-01. A note on the exponential sums of the localized divisor functions. https://arxiv.org/abs/1512.01128

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