p-adic Valuation of Exponential Sums in One Variable Associated to Binomials
, and | Jul 22, 2017
About this article
Article Category: Dedicated to the fifth international conference on Uniform Distribution Theory (UDT 2016) Sopron, Hungary, July 5–8, 2016
Published Online: Jul 22, 2017
Page range: 37 - 53
Received: Jul 08, 2015
Accepted: Dec 16, 2015
DOI: https://doi.org/10.1515/udt-2017-0003
Keywords
© 2017
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.
In this paper we compute the p-adic valuation of exponential sums associated to binomials F(X) = aXd₁ + bXd₂ over Fp. In particular, its p-adic valuation is constant for a, b ∈ F∗p . As a byproduct of our results, we obtain a lower bound for the sizes of value sets of binomials over Fq.