L-functions of symmetric powers of the generalized Airy family of exponential sums: ell-adic and p-adic methods

C. Douglas Haessig, Antonio Rojas-Leon

For ψa nontrivial additive character on the finite field F_q, the map t \mapsto \sum_{x \in F_q} ψ(f(x)+tx) is the Fourier transform of the map t \mapsto ψ(f(t))$. As is well-known…