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Hodge properties of
Airy moments
Claude Sabbah and Jeng-Daw Yu |
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Vol. 5 (2023), No. 2, 215–271
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Abstract |
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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. |
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Keywords
Airy differential equation, mixed Hodge structure,
exponential mixed Hodge structure, irregular Hodge
filtration
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Mathematical Subject Classification
Primary: 14C30, 14D07, 32G20, 32S40, 34M35
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Milestones
Received: 3 January 2022
Revised: 2 October 2022
Accepted: 3 November 2022
Published: 4 June 2023
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Authors |
| Claude Sabbah | |
| Centre de Mathématiques Laurent
Schwartz CNRS, École polytechnique, Institut Polytechnique de Paris France |
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| Jeng-Daw Yu | |
| Department of Mathematics National Taiwan University Taipei Taiwan |
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| © 2023 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). |
