Exact $p$-divisibility of exponential sums via the covering method
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- by Francis Castro and Ivelisse M. Rubio PDF
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Abstract:
In general, the methods to estimate the $p$-divisibility of exponential sums or the number of solutions of systems of polynomial equations over finite fields are non-elementary. In this paper we present the covering method, an elementary combinatorial method that can be used to compute the exact $p$-divisibility of exponential sums over a prime field. The results here allow us to compute the exact $p$-divisibility of exponential sums of new families of polynomials, to unify and improve previously known results, and to construct families of systems of polynomial equations over finite fields that are solvable.References
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Additional Information
- Francis Castro
- Affiliation: Department of Mathematics, University of Puerto Rico, Río Piedras, PO Box 70377, San Juan, Puerto Rico 00936
- Email: franciscastr@gmail.com
- Ivelisse M. Rubio
- Affiliation: Department of Computer Science, University of Puerto Rico, Río Piedras, PO Box 70377, San Juan, Puerto Rico 00936
- MR Author ID: 269818
- Email: iverubio@gmail.com
- Received by editor(s): May 16, 2013
- Received by editor(s) in revised form: July 22, 2013
- Published electronically: October 29, 2014
- Communicated by: Ken Ono
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 143 (2015), 1043-1056
- MSC (2010): Primary 11L03; Secondary 11A07
- DOI: https://doi.org/10.1090/S0002-9939-2014-12315-X
- MathSciNet review: 3293721