S. Brown

collaborators

2 papers

math.NT2026

A proof of Spence's formula using the reciprocity law for Dedekind sums

Steven Brown

In 1963, Edward Spence published a proof of the following With $I ¨ $ being Euler totient function, if $n > 1$ is an integer, and if \begin{equation*} 0<a_1<\cdots<a_{Ï(n)}<n, \end{eq…

math.NT2025

On a family of sums of powers of the floor function and their links with generalized Dedekind sums

Steven Brown

In this paper we are concerned with a family of sums involving the floor function. With $r$ a non negative integer and $n$ and $m$ positive integers we consider the sums \begin{equ…