Hodge properties of Airy moments

Abstract

We consider the complex analogues of symmetric power moments of cubic exponential sums. These are symmetric powers of the classical Airy differential equation. We show that their de Rham cohomologies underlie an arithmetic Hodge structure in the sense of Anderson and we compute their Hodge numbers by means of the irregular Hodge filtration, which is indexed by rational numbers, on their realizations as exponential mixed Hodge structures. The main result is that all Hodge numbers are either zero or one.

arXiv comment47 pages. V2: final published version, 48 pages

References in corpus (7)

• Fourier-Laplace transform of a variation of polarized complex Hodge structure
• Automorphy and irreducibility of some l-adic representations
• On the irregular Hodge filtration of exponentially twisted mixed Hodge modules
• Hodge theory of Kloosterman connections
• Quadratic relations between Bessel moments
• Irregular Hodge theory
• Irregular Hodge numbers of confluent hypergeometric differential equations