Shannon Starr

collaborators

3 papers

math.NT2026

Asymptotics of the d'Arcais Numbers at Small $k$

Shannon Starr

The d'Arcais numbers are the triangular array ${A (2, n, k) : n = 0, 1, \dots, k = 0, \dots, n}$ , such that $\sum_{n=0}^{\infty} \sum_{k=0}^{n} A(2,n,k) x^k z^n/n! = ((z;z)_{\infty})^…

math.PR2026

Large Deviations for the d'Arcais Numbers

Shannon Starr

The d'Arcais polynomials $P_{n} (z)$ for $n \in {0, 1, \dots}$ are defined as $\sum_{n = 0}^{\infty} P_{n} (z) q^{n} = exp (- z ln ((q; q)_{\infty}))$ where the $q$ -Pochhammer symbol is $(q;q)_{\…

math.CO2025

Some Observations about the "Generalized Abundancy Index"

Shannon Starr

Let $A (ℓ, n) \subset S_{n}^{ℓ}$ denote the set of all $ℓ$ -tuples $(π_{1}, \dots, π_{ℓ})$ , for $π_{1}, \dots, π_{ℓ} \in S_{n}$ satisfying: $\forall i < j$ we have $π_iπ_j=…

Asymptotics of the d'Arcais Numbers at Small k

Large Deviations for the d'Arcais Numbers

Some Observations about the "Generalized Abundancy Index"

Asymptotics of the d'Arcais Numbers at Small $k$