<abstract xmlns="http://www.w3.org/1999/xhtml"> 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.</abstract>

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.

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

Uniform distribution theory

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"p-adic Valuation of Exponential Sums in One Variable Associated to Binomials"}

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...

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

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
p-divisibility, exponential sums, value sets

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

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

Keywordsp-divisibility, exponential sums, value sets

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
p-divisibility, exponential sums, value sets