Value distribution of cyclotomic polynomial coefficients
Abstract
Let an(k) be the kth coefficient of the nth cyclotomic polynomial Phin(x). As n ranges over the integers, an(k) assumes only finitely many values. For any such value v we determine the density of integers n such that an(k)=v. Also we study the average of the an(k). We derive analogous results for the kth Taylor coefficient of 1/Phin(x) (taken around x=0), the kth coefficient of the nth reciprocal cyclotomic polynomial. We formulate various open problems.
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