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Symmetric powers of the p-adic Bessel equation. (English) Zbl 0574.12021

We interpret certain functions attached to Kloosterman sums in terms of the Dwork’s cohomology associated to symmetric powers of the Bessel differential module. This allows us to show that these functions are indeed polynomials, to compute their degree, and to prove that they satisfy a functional equation.

MSC:

12H25 \(p\)-adic differential equations
14F30 \(p\)-adic cohomology, crystalline cohomology
11L03 Trigonometric and exponential sums (general theory)
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