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Abstract
The classical Kloosterman sums give rise to a Galois representation of the function field unramified outside 0 and ∞. We study the local monodromy of this representation at ∞ 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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Published Online: 2005-12-20
Published in Print: 2005-12-20
Walter de Gruyter GmbH & Co. KG
