John M. Campbell

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20242026

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math.NT2026

On the binary digits of the ErdÅs-Borwein constant

John M. Campbell

In a landmark paper on arithmetical properties of Lambert series, ErdÅs proved that $\sum_{n = 1}^{\infty} \frac{1}{2 ^{n} - 1}$ is irrational. This value $E$ is now referred to as t…

math.NT2026

On divisor sums due to ErdÅs and Ramanujan

John M. Campbell

Let $d (n)$ denote the number of divisors of a positive integer $n$ . A classical problem in analytic number theory is given by the asymptotic behavior of the divisor sum $\sum_{n \l…

math.NT2024

On the minimal polynomials of the arguments of dilogarithm ladders

John M. Campbell

Letting $L_{n} (N, u)$ denote a polylogarithm ladder of weight $n$ and index $N$ with $u$ as an algebraic number, there is a rich history surrounding how mathematical objects of thi…

On the binary digits of the ErdÅs-Borwein constant

On divisor sums due to ErdÅs and Ramanujan

On the minimal polynomials of the arguments of dilogarithm ladders

On the binary digits of the ErdÅs-Borwein constant

On divisor sums due to ErdÅs and Ramanujan