Power Series Approximations to Fekete Polynomials

2016/11/14 by Jason P. Bell, Bell, Jason, Igor E. Shparlinski +1
Mathematics · #Analytic Number Theory Research #Advanced Mathematical Identities #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1611.04356

Abstract

We study how well Fekete polynomials F_p(X) = ∑_n=0^p-1 ((n)/(p)) Xⁿ ∈ \mathbb Z[X] with the coefficients given by Legendre symbols modulo a prime p, can be approximated by power series representing algebraic functions of a given degree. We also obtain some explicit results describing polynomial recurrence relations which are satisfied by the coefficients of such algebraic functions.

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