Newton polygons for L-functions of generalized Kloosterman sums

L-Functions for Symmetric Products of Kloosterman Sums

The classical Kloosterman sums give rise to a Galois representation of the function field unramfied outside 0 and ∞. We study the local monodromy of this representation at ∞ using l-adic method based on the work of Deligne and Katz. As an application, we determine the degrees and the bad factors of the L-functions of the symmetric products of the above representation. Our results generalize som...

VARIATION OF p -ADIC NEWTON POLYGONS FOR L-FUNCTIONS OF EXPONENTIAL SUMS

Abstract. In this paper, we continue to develop the systematic decomposition theory [18] for the generic Newton polygon attached to a family of zeta functions over finite fields and more generally a family of L-functions of n-dimensional exponential sums over finite fields. Our aim is to establish a new collapsing decomposition theorem (Theorem 3.7) for the generic Newton polygon. A number of a...

Second Moments of Dirichlet L-functions Weighted by Kloosterman Sums

Newton Polygons for Twisted Exponential Sums

We study the p-adic absolute value of the roots of the L-functions associated to certain twisted character sums, and additive character sums associated to polynomials P (x d), when P varies among the space of polynomial of fixed degree e over a finite field of characteristic p. For sufficiently large p, we determine in both cases generic Newton polygons for these L-functions, which is a lower b...

Hodge-stickelberger Polygons for L-functions of Exponential Sums

Let Fq be a finite field of cardinality q and characteristic p. Let P (x) be any one-variable Laurent polynomial over Fq of degree (d1, d2) respectively and p d1d2. For any fixed s ≥ 1 coprime to p, we prove that the q-adic Newton polygon of the L-functions of exponential sums of P (xs) has a tight lower bound which we call Hodge-Stickelberger polygon, depending only on the d1, d2, s and the re...