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arXiv:1501.07502math.NT

Introducing an Analysis in Finite Fields

H. M. de Oliveira, R. M. Campello de Souza

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Abstract

Looking forward to introducing an analysis in Galois Fields, discrete functions are considered (such as transcendental ones) and MacLaurin series are derived by Lagrange's Interpolation. A new derivative over finite fields is defined which is based on the Hasse Derivative and is referred to as negacyclic Hasse derivative. Finite field Taylor series and alpha-adic expansions over GF(p), p prime, are then considered. Applications to exponential and trigonometric functions are presented. Theses tools can be useful in areas such as coding theory and digital signal processing.

arXiv comments
6 pages, 1 figure. Conference: XVII Simposio Brasileiro de Telecomunicacoes, 1999, Vila Velha, ES, Brazil. (pp.472-477)
Journal reference
DOI
Subjects
math.NTNumber Theory

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  1. All you need is λ, part one: booleans 1 comment

    • (I’ve also been wondering for a few years whether it is possible to make a version of quantum mechanics which works with the wavefunctions taking on values from a (very large) finite field instead of the complex numbers. My impression so far is “probably not” because you need…

      drdecaView on HNParent context

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