Two explicit divisor sums
Michaela Cully-Hugill, Timothy Trudgian

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 and , where is the number of divisors of and is the number of ways of writing 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.
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