Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-23T08:32:06.777Z Has data issue: false hasContentIssue false
  • English
  • Français

On the growth of the cyclotomic polynomial in the interval (0, 1)

Published online by Cambridge University Press:  18 May 2009

P. Erdös
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let

be the rath cyclotomic polynomial, and denote by An the absolute value of the largest coefficient of Fn(x).Schur proved that

and Emma Lehmer [5] showed that An>cn1/3 for infinitely many n; in fact she proved that n can be chosen as the product of three distinct primes. I proved [3] that there exists a positive constant q such that, for infinitely many n

and Bateman [1] proved very simply that, for every ∈>0 and all n>no(∈),

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 3 , Issue 2 , June 1957 , pp. 102 - 104
Copyright
Copyright © Glasgow Mathematical Journal Trust 1957

References

1.Bateman, P. T., Note on the coefficients of the cyclotomic polynomial, Bull. Amer. Math. Soc. 55 (1949), 1180–1181.CrossRefGoogle Scholar
2.Erdös, P., On the coefficients of the cyclotomic polynomial, Bull. Amer. Math. Soc., 52 (1946), 179–184.CrossRefGoogle Scholar
3.Erdös, P., On the coefficients of the cyclotomic polynomial, Portugaliae Math., 8 (1949), 63–71.Google Scholar
4.Lehmer, D. H., The distribution of totatives, Canadian Math. J., 7 (1955), 347–357.CrossRefGoogle Scholar
5.Lehmer, Emma, On the magnitude of the coefficients of the cyclotomic polynomial, Bull. Amer. Math. Soc. 42 (1936), 389–392.CrossRefGoogle Scholar
6.Vijayaraghavan, T., On a problem in elementary number theory, J. Indian Math. Soc. (N.S.), 15 (1951), 51–56.Google Scholar