28 citations · 96 across the 11 of their papers we have counts for
11 papers
Resurgent Lambert series from Feynman and beyond
David Broadhurst, Daniele Dorigoni
Lambert series of the form are ubiquitous in mathematical physics. In particular, 2-loop sunrise and 3-loop banana Feynman diagrams yield Lambert series…
Polynomials and asymptotic constants in a resurgent problem from 't Hooft
David Broadhurst, Gergő Nemes
In a recent study of the quantum theory of harmonic oscillators, Gerard 't Hooft proposed the following problem: given for , find its a…
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 . For…
Number of partitions of modular integers (with an Appendix by P. Deligne)
David Broadhurst, Xavier Roulleau
For integers , we give a formula for the number of order subsets of the ring whose sum of elements is modulo . To do so, we de…
Five families of rapidly convergent evaluations of zeta values
David Broadhurst
This work derives 5 methods to evaluate families of odd zeta values by combining a power of with Lambert series whose ratios of successive terms tend to with i…
Richard Feynman's talent for finding things out
David Broadhurst
This article is a summary of a talk about Richard Feynman, given at a conference Polymaths across the Eras organized in November 2023 by the St Cross Centre for the History and Phi…
Comparison of the Gottfried and Adler sum rules within the large-Nc expansion
D. J. Broadhurst, A. L. Kataev, C. J. Maxwell
The Adler sum rule for deep inelastic neutrino scattering measures the isospin of the nucleon and is hence exact. By contrast, the corresponding Gottfried sum rule for charged lept…
Where do the tedious products of zetas come from?
D. J. Broadhurst
Lamentably, the full analytical content of the epsilon-expansion of the master two-loop two-point function, with arbitrary self-energy insertions in 4-2epsilon dimensions, is still…
Bjorken unpolarized and polarized sum rules: comparative analysis of large-N_F expansions
D. J. Broadhurst, A. L. Kataev
Analytical all-orders results are presented for the one-renormalon-chain contributions to the Bjorken unpolarized sum rule for the F_1 structure function of nu N deep-inelastic sca…
Solving differential equations for 3-loop diagrams: relation to hyperbolic geometry and knot theory
D. J. Broadhurst
In hep-th/9805025, a result for the symmetric 3-loop massive tetrahedron in 3 dimensions was found, using the lattice algorithm PSLQ. Here we give a more general formula, involving…
Compact analytical form for non-zeta terms in critical exponents at order 1/N^3
D. J. Broadhurst, A. V. Kotikov
We simplify, to a single integral of dilogarithms, the least tractable O(1/N^3) contribution to the large-N critical exponent of the non-linear sigma-model, and hence -the…