https://hal-polytechnique.archives-ouvertes.fr/hal-03752512Sabbah, ClaudeClaudeSabbahCMLS - Centre de MathÃ©matiques Laurent Schwartz - X - Ã‰cole polytechnique - CNRS - Centre National de la Recherche ScientifiqueYu, Jeng-DawJeng-DawYuHodge properties of Airy momentsHAL CCSD2022[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]Sabbah, Claude2022-08-16 21:55:262023-02-08 17:11:252022-08-16 21:55:26enPreprints, Working Papers, ...1We 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.