Heights of divisors of x^n-1

Details Heights of divisors of x^n-1 Heights of divisors of x^n-1

2011-11-23

arxiv.org/abs/1111.5404v1

Integers 11A. Proceedings of the Integers Conference 2009 (2011). Article 20, 1-9

Mathematics

Number Theory

8 pages

Scientific paper

The height of a polynomial with integer coefficients is the largest coefficient in absolute value. Many papers have been written on the subject of bounding heights of cyclotomic polynomials. One result, due to H. Maier, gives a best possible upper bound of n^{\psi(n)} for almost all n, where \psi(n) is any function that approaches infinity as n tends to infinity. We will discuss the related problem of bounding the maximal height over all polynomial divisors of x^n - 1 and give an analogue of Maier's result in this scenario.

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