INTEGERS 11 A ( 2011 ) Proceedings of Integers Conference 2009 HEIGHTS OF DIVISORS OF X n − 1
نویسنده
چکیده
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 nψ(n) for almost all n, where ψ(n) is any function that approaches infinity as n → ∞. We will discuss the related problem of bounding the maximal height over all polynomial divisors of xn − 1 and give an analogue of Maier’s result in this scenario. – For my adviser Carl Pomerance on his 65th birthday
منابع مشابه
9 INTEGERS 11 A ( 2011 ) Proceedings of Integers Conference 2009
We study the question of whether for each n there is an m �= n with λ(m) = λ(n), where λ is Carmichael’s function. We give a “near” proof of the fact that this is the case unconditionally, and a complete conditional proof under the Extended Riemann Hypothesis. –To Professor Carl Pomerance on his 65th birthday
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