Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Functional Equations of $L$-Functions for Symmetric Products of the
  Kloosterman Sheaf   We determine the (arithmetic) local monodromy at 0 and at $\infty$ of the
Kloosterman sheaf using local Fourier transformations and Laumon's stationary
phase principle. We then calculate $\epsilon$-factors for symmetric products of
the Kloosterman sheaf. Using Laumon's product formula, we get functional
equations of $L$-functions for these symmetric products, and prove a conjecture
of Evans on signs of constants of functional equations.

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The categories of this paper are: hep-th
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The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex