David J. Broadhurst

works on

eisenstein series 1 feynman diagrams 1 lambert series 1 modular forms 1 resurgence 1 topological strings 1

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math.NT2025

Polynomials and asymptotic constants in a resurgent problem from 't Hooft

David Broadhurst, GergÅ Nemes, Gergő Nemes

In a recent study of the quantum theory of harmonic oscillators, Gerard 't Hooft proposed the following problem: given $G (z) = \sum_{n = 1}^{\infty} n z^{n}$ for $∣ z ∣ < 1$ , find its a…

math.NT2025

Resurgent Lambert series with characters

David Broadhurst, Daniele Dorigoni

We consider certain Lambert series as generating functions of divisor sums twisted by Dirichlet characters and compute their exact resurgent transseries expansion near $q = 1^{-}$ . For…

math.NT2025

Number of partitions of modular integers (with an Appendix by P. Deligne)

David Broadhurst, Xavier Roulleau

For integers $n, k, s$ , we give a formula for the number $T (n, k, s)$ of order $k$ subsets of the ring $Z / n Z$ whose sum of elements is $s$ modulo $n$ . To do so, we de…