On the variance of sums of divisor functions in short intervals

Stephen Lester

On the variance of sums of divisor functions in short intervals

Number Theory 2015-02-05 v1

Authors: Stephen Lester

Abstract

Given a positive integer $n$ the $k$ -fold divisor function $d_k(n)$ equals the number of ordered $k$ -tuples of positive integers whose product equals $n$ . In this article we study the variance of sums of $d_k(n)$ in short intervals and establish asymptotic formulas for the variance of sums of $d_k(n)$ in short intervals of certain lengths for $k=3$ and for $k \ge 4$ under the assumption of the Lindel\"of hypothesis.

Keywords

divisor function variance short intervals asymptotic formulas Lindelöf hypothesis number theory

Cite

@article{arxiv.1502.01170,
  title  = {On the variance of sums of divisor functions in short intervals},
  author = {Stephen Lester},
  journal= {arXiv preprint arXiv:1502.01170},
  year   = {2015}
}

Comments

13 pages

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