On the L-functions of power moments of Kloosterman sums


Prof. Jeng-Daw Yu  ( Department of Mathematics, National Taiwan University )

10:30:00 - 11:30:00
103 , Mathematics Research Center Building (ori. New Math. Bldg.)

D.Broadhurst observed the shape of the conjectural completed L-functions attached to symmetric power moments of Kloosterman sums via numerical computation. We provide the proof of part of the observations by constructing the underlying motives and verifying their automorphy. Our approach involves ideas and tools in exponential motives and irregular Hodge theory. This is joint work with J.Fresán and C.Sabbah.