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- W1714892479 abstract "For psi a nontrivial additive character on the finite field F_q, the map t mapsto sum_{x in F_q} psi(f(x)+tx) is the Fourier transform of the map t mapsto psi(f(t))$. As is well-known, this has a cohomological interpretation, producing a continuous ell-adic Galois representation. This paper studies the L-function attached to the k-th symmetric power of this representation using both ell-adic and p-adic methods. Using ell-adic techniques, we give an explicit formula for the degree of this L-function and determine the complex absolute values of its roots. Using p-adic techniques, we study the p-adic absolute values of the roots." @default.
- W1714892479 created "2016-06-24" @default.
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- W1714892479 date "2009-08-09" @default.
- W1714892479 modified "2023-09-27" @default.
- W1714892479 title "L-functions of symmetric powers of the generalized Airy family of exponential sums: ell-adic and p-adic methods" @default.
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