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math.NT2026
On the calculation of an integral introduced by Hubert Delange
Steven Brown
In his paper, ''Sur la distribution des fractions irréductibles de dénominateur ou de dénominateur au plus égal à '', Hubert Delange considers the family integrals defined b…
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 being Euler totient function, if is an integer, and if \begin{equation*} 0<a_1<\cdots<a_{ϕ(n)}<n, \end{equa…
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 a non negative integer and and positive integers we consider the sums \begin{equ…