Improved Lower Bound for the Mahler Measure of the Fekete Polynomials Academic Article

abstract

• 2017, Springer Science+Business Media, LLC. We show that there is an absolute constant c> 1 / 2 such that the Mahler measure of the Fekete polynomials fp of the form fp(z):=k=1p-1(kp)zk(where the coefficients are the usual Legendre symbols) is at least cp for all sufficiently large primes p. This improves the lower bound (12-)p known before for the Mahler measure of the Fekete polynomials fp for all sufficiently large primes p c. Our approach is based on the study of the zeros of the Fekete polynomials on the unit circle.

authors

• Erdelyi, Tamas

published proceedings

• CONSTRUCTIVE APPROXIMATION

author list (cited authors)

• Erdelyi, T.

citation count

• 3

complete list of authors

• Erdélyi, Tamás

publication date

• October 2018

publisher

• Springer Nature  Publisher

published in

• Constructive Approximation  Journal

keywords

• Fekete Polynomials
• Legendre Symbols
• Mahler Measure
• Number Of Zeros On The Unit Circle
• Polynomials
• Restricted Coefficients

Digital Object Identifier (DOI)

• 10.1007/s00365-017-9398-y

start page

• 283

end page

• 299

volume

• 48

issue

• 2

URL

• http://dx.doi.org/10.1007/s00365-017-9398-y