L-functions of symmetric power moments of Kloosterman sums

This talk will revolve around a global family of L-functions built up by assembling symmetric power moments of Kloosterman sums over finite fields. We prove that they arise from potentially automorphic motives over the rational numbers, and hence admit a meromorphic extension to the complex plane which satisfies the expected functional equation. Although the motives turn out to be "classical", the strategy consists in first realising them as exponential motives and computing the Hodge numbers by means of the irregular Hodge filtration. It is a joint work with Claude Sabbah and Jeng-Daw Yu.