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

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.

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

Johann Radon Institute for Comput. and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstr. 69, 4040 Linz,

Uniform distribution theory

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

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.

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

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

Keywordspolynomials, 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.

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