Two explicit divisor sums

TL;DR

This paper provides explicit bounds on divisor sums involving $d(n)^2$ and $d_4(n)$, improving bounds related to class numbers of quartic number fields, with implications for number theory.

Contribution

It offers new explicit bounds on divisor sums and refines the upper bounds for class numbers of quartic number fields.

Findings

Explicit bounds on sums of $d(n)^2$ and $d_4(n)$

Improved upper bounds for class numbers of quartic fields

Enhanced understanding of divisor sum behaviors

Abstract

We give explicit bounds on sums of $d(n)^2$ and $d_4(n)$, where $d(n)$ is the number of divisors of $n$ and $d_4(n)$ is the number of ways of writing $n$ as a product of four numbers. In doing so we make a slight improvement on the upper bound for class numbers of quartic number fields.