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

Francis N. Castro

Francis N. Castro

Department of Mathematics University of Puerto Rico Río Piedras P. O.Box 70377Puerto Rico, U.S.A
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Castro, Francis N.
, 
Raúl Figueroa

Raúl Figueroa

Department of Mathematics University of Puerto Rico Río Piedras P. O.Box 70377Puerto Rico, U.S.A
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Figueroa, Raúl
 and 
Puhua Guan

Puhua Guan

Department of Mathematics University of Puerto Rico Río Piedras P. O.Box 70377Puerto Rico, U.S.A
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Guan, Puhua
  
Jul 22, 2017
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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.

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English
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2 times per year
Journal Subjects:
Mathematics, Algebra and Number Theory, Discrete Mathematics, Probability and Statistics, Numerical and Computational Mathematics
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