John M. Campbell

activity

20242026

collaborators

5 papers

math.CO2026

The finitude of the fibers of the complementary Bell numbers

John M. Campbell

Subbarao and Verma introduced, in 1999, a number of open problems concerning the sequence $(f (n))_{n \geq 0}$ of complementary Bell numbers, which may be defined via Bell polynomia…

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.CA2025

$q$ -analogues of $I ¨ $ -formulas due to Ramanujan and Guillera

John M. Campbell

The first known $q$ -analogues for any of the $17$ formulas for $\frac{1}{I ¨} $ due to Ramanujan were introduced in 2018 by Guo and Liu (J. Difference Equ. Appl. 29:505-513, 2018), via…

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…

The finitude of the fibers of the complementary Bell numbers

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

On divisor sums due to ErdÅs and Ramanujan

q-analogues of I¨-formulas due to Ramanujan and Guillera

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

$q$ -analogues of $I ¨ $ -formulas due to Ramanujan and Guillera