We prove sieve-type lower bounds for the Mahler measure of polynomials on subarcs of the unit circle of the complex plane. This is then applied to give an essentially sharp lower bound for the Mahler measure of the Fekete polynomials on subarcs.

Abstract. In this present investigation, authors introduce certain subclasses of starlike and convex functions of complex order b, using a linear multiplier differential operator D λ,μf(z). In this paper, for these classes the Fekete–Szegö problem is completely solved. Various new special cases of our results are also pointed out.

Fekete polynomials associate with each prime number p a polynomial coefficients −1 or 1 except the constant term, which is 0. These reflect distribution of quadratic residues modulo p. were already considered in 19th century relation to studies Dirichlet L-functions. In our paper, we introduce two closely related polynomials. We then express their special values at several integers terms certai...