Large Deviations for the d'Arcais Numbers
Abstract
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 $(q;q)_{\infty} = \prod_{k=1}^{\infty} (1-q^k)$ for $|q|
Fields of Study & Subjects
Advanced Mathematical Identities
Analytic Number Theory Research
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 12 January 2026
- Language
- EN
- Document type
- Preprint