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Hodge theory of Kloosterman connections

Abstract : We construct motives over the rational numbers associated with symmetric power moments of Kloosterman sums, and prove that their L-functions extend meromorphically to the complex plane and satisfy a functional equation conjectured by Broadhurst and Roberts. Although the motives in question turn out to be "classical", the strategy consists in first realizing them as exponential motives and computing their Hodge numbers by means of the irregular Hodge filtration. We show that all Hodge numbers are either zero or one, which implies potential automorphy thanks to recent results of Patrikis and Taylor.
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Preprints, Working Papers, ...
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https://hal-polytechnique.archives-ouvertes.fr/hal-02322250
Contributor : Claude Sabbah <>
Submitted on : Monday, October 21, 2019 - 3:42:39 PM
Last modification on : Saturday, August 1, 2020 - 10:42:02 AM

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  • HAL Id : hal-02322250, version 1
  • ARXIV : 1810.06454

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Javier Fresán, Claude Sabbah, Jeng-Daw Yu. Hodge theory of Kloosterman connections. 2019. ⟨hal-02322250⟩

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