Translator Disclaimer
1 June 2022 Hodge theory of Kloosterman connections
Javier Fresán, Claude Sabbah, Jeng-Daw Yu
Author Affiliations +
Duke Math. J. 171(8): 1649-1747 (1 June 2022). DOI: 10.1215/00127094-2021-0036

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,” we compute their Hodge numbers by means of the irregular Hodge filtration on their realizations as exponential mixed Hodge structures. We show that all Hodge numbers are either zero or one, which implies potential automorphy thanks to recent results of Patrikis and Taylor.

Citation

Download Citation

Javier Fresán. Claude Sabbah. Jeng-Daw Yu. "Hodge theory of Kloosterman connections." Duke Math. J. 171 (8) 1649 - 1747, 1 June 2022. https://doi.org/10.1215/00127094-2021-0036

Information

Received: 4 December 2018; Revised: 14 April 2021; Published: 1 June 2022
First available in Project Euclid: 4 May 2022

Digital Object Identifier: 10.1215/00127094-2021-0036

Subjects:
Primary: 11G40
Secondary: 11F80 , 11L05 , 14F40 , 32S35 , 32S40

Keywords: connections with irregular singularities , D-modules , exponential motives , Fourier transform , Galois representations , irregular Hodge filtration , Kloosterman sums , ℓ-adic sheaves , L-functions , mixed Hodge modules , potential automorphy

Rights: Copyright © 2022 Duke University Press

JOURNAL ARTICLE
99 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.171 • No. 8 • 1 June 2022
Back to Top