Leírás
Austrian-Hungarian Diophantine Number Theory seminar
https://uni-salzburg.webex.com/uni-salzburg/j.php?MTID=m17cbc4321f9834a1d11c14225a19805a
Abstract: I will speak on a recent work with Florian Luca, where we show that, apart some obvious exceptions, the polynomials of the form a(x)f(x)n+b(x)g(x)n cannot vanish at roots of unity of order exceeding some effective constant. The qualitative result follows from the Bombieri-Masser-Zannier work on unlikely intersections, but our contribution is making this effective (in fact, totally explicit), which, to our knowledge, cannot be deduced from any available version of the BMZ or similar theorem. Our principal tools are Schinzel's theorem on primitive divisors, and Mann's theorem on vanishing sums of roots of unity.