Improved Lower Bound for the Mahler Measure of the Fekete Polynomials
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© 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-ε)p known before for the Mahler measure of the Fekete polynomials fp for all sufficiently large primes p≥ cε. Our approach is based on the study of the zeros of the Fekete polynomials on the unit circle.
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