https://scholars.lib.ntu.edu.tw/handle/123456789/634457
Title: | Hodge properties of Airy moments | Authors: | Claude Sabbah JENG-DAW YU |
Keywords: | Airy differential equation | exponential mixed Hodge structure | irregular Hodge filtration | mixed Hodge structure; Mathematics - Algebraic Geometry; Mathematics - Algebraic Geometry; Mathematics - Number Theory; 14C30, 14D07, 32G20, 32S40, 34M35 | Issue Date: | 26-Dec-2021 | Journal Volume: | 5 | Journal Issue: | 2 | Source: | Tunisian J. Math. 5 (2023) 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. |
Description: | 47 pages. V2: final published version, 48 pages |
URI: | https://scholars.lib.ntu.edu.tw/handle/123456789/634457 | ISSN: | 25767658 | DOI: | 10.2140/tunis.2023.5.215 |
Appears in Collections: | 數學系 |
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