Article
Value Distribution of Cyclotomic Polynomial Coefficients
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Abstract
Let an(k) be the kth coefficient of the nth cyclotomic polynomial Φn(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/Φn(x) (taken around x = 0). We formulate various open problems.
Keywords
Coefficient of cyclotomic polynomial, prime, density, partition.
Citation
Gallot, Y., Moree, P., & Hommersom, H. (2011). Value distribution of cyclotomic polynomial coefficients. Uniform Distribution Theory, 6(2), 177–206.
Y. Gallot, P. Moree and H. Hommersom, “Value distribution of cyclotomic polynomial coefficients,” Uniform Distribution Theory, vol. 6, no. 2, pp. 177–206, 2011.
Gallot Y, Moree P, Hommersom H. Value distribution of cyclotomic polynomial coefficients. Uniform Distribution Theory. 2011;6(2):177–206.
Gallot, Y., Moree, P. and Hommersom, H. (2011), ‘Value distribution of cyclotomic polynomial coefficients’, Uniform Distribution Theory, 6(2), pp. 177–206.
Gallot, Yves, et al. “Value Distribution of Cyclotomic Polynomial Coefficients.” Uniform Distribution Theory, vol. 6, no. 2, 2011, pp. 177–206.
Gallot, Yves, Pieter Moree, and Huib Hommersom. “Value Distribution of Cyclotomic Polynomial Coefficients.” Uniform Distribution Theory 6, no. 2 (2011): 177–206.
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Published by: Engineering Journals
