Merit Factors of Polynomials Formed by Jacobi Symbols

Abstract

AbstractWe give explicit formulas for the L4 norm (or equivalently for the merit factors) of various sequences of polynomials related to the polynomialsandwhere is the Jacobi symbol.Two cases of particular interest are when N = pq is a product of two primes and p = q + 2 or p = q + 4. This extends work of Høholdt, Jensen and Jensen and of the authors.This study arises from a number of conjectures of Erdȍs, Littlewood and others that concern the norms of polynomials with −1, 1 coefficients on the disc. The current best examples are of the above form when N is prime and it is natural to see what happens for composite N.