Download this article
 Download this article For screen
For printing
Recent Issues
Volume 6, Issue 2
Volume 6, Issue 1
Volume 5, Issue 4
Volume 5, Issue 3
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the journal
Ethics and policies
Peer-review process
Statement, 2023
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 2576-7666
ISSN (print): 2576-7658
Author index
To appear
 
Other MSP Journals
Hodge properties of Airy moments

Claude Sabbah and Jeng-Daw Yu

Vol. 5 (2023), No. 2, 215–271
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.

Keywords
Airy differential equation, mixed Hodge structure, exponential mixed Hodge structure, irregular Hodge filtration
Mathematical Subject Classification
Primary: 14C30, 14D07, 32G20, 32S40, 34M35
Milestones
Received: 3 January 2022
Revised: 2 October 2022
Accepted: 3 November 2022
Published: 4 June 2023
Authors
Claude Sabbah
Centre de Mathématiques Laurent Schwartz
CNRS, École polytechnique, Institut Polytechnique de Paris
France
Jeng-Daw Yu
Department of Mathematics
National Taiwan University
Taipei
Taiwan