On the Periods of Twisted Moments of the Kloosterman Connection

Abstract

This paper aims to study the Betti homology and de Rham cohomology of twisted symmetric powers of the Kloosterman connection of rank two on the torus. We compute the period pairing and, with respect to certain bases, interpret these associated period numbers in terms of the Bessel moments. Via the rational structures on Betti homology and de Rham cohomology, we prove the $\mathbb{Q}$-linear and quadratic relations among these Bessel moments.

40 pages

References in corpus (7)

• Elliptic integral evaluations of Bessel moments
• Hodge theory of Kloosterman connections
• Wrońskian factorizations and Broadhurst-Mellit determinant formulae
• Quadratic relations between Bessel moments
• Quadratic relations between periods of connections
• Hilbert Transforms and Sum Rules of Bessel Moments
• $\mathbb{Q}$-linear dependence of certain Bessel moments