L-Functions for Symmetric Products of Kloosterman Sums

Details L-Functions for Symmetric Products of Kloosterman Sums L-Functions for Symmetric Products of Kloosterman Sums

2004-09-20

arxiv.org/abs/math/0409372v2

Mathematics

Number Theory

25 pages

Scientific paper

The classical Kloosterman sums give rise to a Galois representation of the function field unramfied outside 0 and $\infty$. We study the local monodromy of this representation at $\infty$ using $l$-adic method based on the work of Deligne and Katz. As an application, we determine the degrees and the bad factors of the $L$-functions of the symmetric products of the above representation. Our results generalize some results of Robba obtained through $p$-adic method.

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