J. Campbell

activity

20232026

most citedA generalization of immanants based on partition algebra characters

3 citations · 3 across the 9 of their papers we have counts for

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math.NT2026

Disproofs of two conjectures concerning nondeficient numbers

John M. Campbell

A positive integer $n$ is said to be nondeficient if $σ (n) \geq 2 n$ . Letting the positive divisors of a positive integer $n$ be written as $1 = d_0 < d_1 < \cdots < d_k < d_{k+1} =…

math.CO2026

The construction of $q$ -analogues via $_{3} ϕ_{2}$ -series and $q$ -difference equations

John M. Campbell

We apply the EKHAD-normalization method given in our recent work to obtain, via the $q$ -version of Zeilberger's algorithm, $q$ -WZ pairs $(F, G)$ such that $\sum_{k = 0}^{\infty} F(…

math.NT2026

Quadratic irrational analogues of Ramanujan's series for $1/ π$

John M. Campbell, Shaun Cooper, Dongxi Ye

About 40 years ago Jonathan and Peter Borwein discovered the series identity $n = 0 \sum \infty \frac{( - 1 ) ^{n} ( 6 n )!}{( 3 n )! ( n ! ) ^{3}} \frac{( A + n B )}{C ^{n + 1/2}} = \frac{1}{12 π}$ where…

Disproofs of two conjectures concerning nondeficient numbers

The construction of q-analogues via 3​ϕ2​-series and q-difference equations

Quadratic irrational analogues of Ramanujan's series for 1/π

The construction of $q$ -analogues via $_{3} ϕ_{2}$ -series and $q$ -difference equations

Quadratic irrational analogues of Ramanujan's series for $1/ π$