A note on the exponential sums of the localized divisor functions

Giovanni Coppola; Maurizio Laporta

A note on the exponential sums of the localized divisor functions

Number Theory 2019-04-25 v1

Authors: Giovanni Coppola , Maurizio Laporta

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, $d_k(n)$ .

Keywords

exponential sum localized divisor function k-divisor function number theory upper bound counting function

Cite

@article{arxiv.1512.01128,
  title  = {A note on the exponential sums of the localized divisor functions},
  author = {Giovanni Coppola and Maurizio Laporta},
  journal= {arXiv preprint arXiv:1512.01128},
  year   = {2019}
}

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A note on the exponential sums of the localized divisor functions

Abstract

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