Some conjectures on the maximal height of divisors of $x^n-1$

Details Some conjectures on the maximal height of divisors of $x^n-1$ Some conjectures on the maximal height of divisors of $x^n-1$

2010-09-29

arxiv.org/abs/1009.5970v1

Mathematics

Number Theory

Scientific paper

Define B(n) to be the largest height of a polynomial in $\mathbb{Z}[x]$
dividing $x^n-1$. We formulate a number of conjectures related to the value of
B(n) when $n$ is of a prescribed form. Additionally, we prove a lower bound for
$B(p^aq^b)$ where $p,q$ are distinct primes.

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