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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.
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Preprints, Working Papers, ...
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https://hal-polytechnique.archives-ouvertes.fr/hal-03752512
Contributor : Claude Sabbah Connect in order to contact the contributor
Submitted on : Tuesday, August 16, 2022 - 9:55:26 PM
Last modification on : Wednesday, August 17, 2022 - 3:39:05 AM

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  • HAL Id : hal-03752512, version 1
  • ARXIV : 2112.13405

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Claude Sabbah, Jeng-Daw Yu. Hodge properties of Airy moments. 2022. ⟨hal-03752512⟩

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