Recently, Broadhurst studied the L-functions associated with symmetric powers of Kloosterman sums and conjectured a functional equation. We show how the irregular Hodge filtration allows one to “explain” the gamma factors at infinity in a similar way to Serre's recipe for usual motives (ongoing joint work with Claude Sabbah and Jeng-Daw Yu).
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/5312