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On the Pseudorandomness of the Liouville Function of Polynomials over a Finite Field

László Mérai

Mérai, László

and

Winterhof, Arne

Jan 13, 2017

On the Pseudorandomness of the Liouville Function of Polynomials over a Finite Field's Cover Image

Uniform distribution theory

Volume 11 (2016): Issue 1 (June 2016)

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Published Online: Jan 13, 2017

Page range: 47 - 58

Received: Apr 27, 2015

Accepted: Aug 31, 2015

DOI: https://doi.org/10.1515/udt-2016-0004

Keywords
polynomials, finite fields, irreducible factors, pseudorandom sequence, balancedness, well-distribution, correlation measure, linear complexity, polynomial Liouville function, polynomial Möbius function

© 2016 László Mérai et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

We study several pseudorandom properties of the Liouville function and the Möbius function of polynomials over a finite field. More precisely, we obtain bounds on their balancedness as well as their well-distribution measure, correlation measure, and linear complexity profile.

Language:: English

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

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