Large cyclotomic coefficients


Il 27 marzo alle 14.30 in aula 1A/150, il Prof. Pieter Moree
(Max Planck Institute, Bonn) terra' un seminario intitolato
"Large cyclotomic coefficients".

The smallness of coefficients of cyclotomic polynomials $Phi_n(x)$ already fascinated mathematicians in the 19th century. It is not so difficult to prove that if the coefficients are not in ${-1,0,1}$ then $n$ must have at least three distinct odd prime divisors. Thus the easiest non-trivial cases is where $n=pqr$ with $2In 1968 Sister Marion Beiter conjectured that the coefficients of a ternary cyclotomic polynomial are $leq (p+1)/2$ in absolute value. Since then various partial positive results have been obtained.
However, recently I showed, jointly with Yves Gallot, that in general the Beiter conjecture is `very wrong'. The talk should be understandable also to people with little previous background in number theory.

Rif. int. A. Languasco

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