Hilbert Transforms and Sum Rules of Bessel Moments

Abstract

Using Hilbert transforms, we establish two families of sum rules involving Bessel moments, which are integrals associated with Feynman diagrams in two-dimensional quantum field theory. With these linear relations among Bessel moments, we verify and generalize two conjectures by Bailey-Borwein-Broadhurst-Glasser and Broadhurst-Mellit.

(v1) 9 pages. Verification and generalization of the integrality for Crandall numbers (OEIS A262961) (v2) 10 pages. Minor corrections and additions. Revised according to referee's report

References in corpus (2)

• Elliptic integral evaluations of Bessel moments
• Wick rotations, Eichler integrals, and multi-loop Feynman diagrams

Cited by in corpus (5)

• Quadratic relations between Bessel moments
• Some algebraic and arithmetic properties of Feynman diagrams
• On Laporta's 4-loop sunrise formulae
• $\mathbb{Q}$-linear dependence of certain Bessel moments
• On the Periods of Twisted Moments of the Kloosterman Connection