Moments of Bessel functions are expected to occur in the finite part of certain Feynman integrals, and it is thus of interest to physicists to evaluate them precisely. A paper by Bailey Borwein Broadhurst and Glasser (ArXiV:0801.0891) contains a large collection of beautiful expressions for these moments. In the simplest cases, the Bessel moments are multiples of pi by algebraic numbers, but in more elaborate examples the formulas start to involve special values of L-functions, elliptic integrals and values of hypergeometric functions, all of which are classical periods associated with algebraic varieties defined over number fields.I will explain why it is no accident that Bessel moments, and indeed many other similar definite integrals produce period numbers, and which algebraic varieties they come from.
Moments of Bessel functions and period numbers
28.10.2025 13:15 - 14:45
Organiser:
H. Grobner, A. Minguez-Espallargas, A. Mellit
Location: