p-adic Valuation of Exponential Sums in One Variable Associated to Binomials

Francis N. Castro; Raúl Figueroa; Puhua Guan

doi:10.1515/udt-2017-0003

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p-adic Valuation of Exponential Sums in One Variable Associated to Binomials

Uniform distribution theory

Volume 12 (2017): Issue 1 (June 2017)

By: Francis N. Castro, Raúl Figueroa and Puhua Guan

Open Access

|Jul 2017

Abstract

In this paper we compute the p-adic valuation of exponential sums associated to binomials F(X) = aX^d₁ + bX^d₂ over F_p. 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 F_q.

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Articles in this issue

DOI: https://doi.org/10.1515/udt-2017-0003 | Journal eISSN: 2309-5377 | Journal ISSN: 1336-913X

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Language: English

Page range: 37 - 53

Submitted on: Jul 8, 2015

Accepted on: Dec 16, 2015

Published on: Jul 22, 2017

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

Related subjects:

Algebra and number theory,

Discrete mathematics,

Probability and statistics,

Numerical and computational mathematics

© 2017 Francis N. Castro, Raúl Figueroa, Puhua Guan, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 12 (2017): Issue 1 (June 2017)