The Mahler Measure of the Rudin-Shapiro Polynomials Academic Article

abstract

• 2015, Springer Science+Business Media New York. Littlewood polynomials are polynomials with each of their coefficients in { - 1 , 1 }. A sequence of Littlewood polynomials that satisfies a remarkable flatness property on the unit circle of the complex plane is given by the RudinShapiro polynomials. It is shown in this paper that the Mahler measure and the maximum modulus of the RudinShapiro polynomials on the unit circle of the complex plane have the same size. It is also shown that the Mahler measure and the maximum norm of the RudinShapiro polynomials have the same size even on not too small subarcs of the unit circle of the complex plane. Not even nontrivial lower bounds for the Mahler measure of the RudinShapiro polynomials have been known before.

authors

• Erdelyi, Tamas

published proceedings

• CONSTRUCTIVE APPROXIMATION

author list (cited authors)

• Erdelyi, T.

citation count

• 6

complete list of authors

• Erdélyi, Tamás

publication date

• June 2016

publisher

• Springer Nature  Publisher

published in

• Constructive Approximation  Journal

keywords

• Littlewood Polynomials
• Mahler Measure
• Rudin-shapiro Polynomials

Digital Object Identifier (DOI)

• 10.1007/s00365-015-9297-z

start page

• 357

end page

• 369

volume

• 43

issue

• 3

URL

• http://dx.doi.org/10.1007/s00365-015-9297-z