We consider the complex analogues of symmetric power moments of cubic exponential
sums. These are symmetric powers of the classical Airy differential equation. We show that …

The L-function of symmetric powers of classical Kloosterman sums is a polynomial whose
degree is now known, as well as the complex absolute values of the roots. In this paper, we …

We consider arbitrary algebraic families of lower order deformations of nondegenerate toric
exponential sums over a finite field. We construct a relative polytope with the aid of which we …

The symmetric power L-function of the hyper-Kloosterman family is a rational function over
the integers. Its degree and complex absolute values of its zeros and poles are now known …

We study the p-adic valuations of roots of L-functions associated with certain families of
exponential sums of Laurent polynomials f∈ Fq [x±11,..., x±1n]. The families we consider …

In this paper we give a modular interpretation of the k-th symmetric power L-function of the
Kloosterman family of exponential sums in characteristics 2 and 3, and in the case of p= 2 …

We prove some improvements of the classical Weil bound for one variable additive and
multiplicative character sums associated to a polynomial over a finite field $ k=\Fq $ for two …