Leírás
Austrian-Hungarian Diophantine Number Theory seminar
https://uni-salzburg.webex.com/uni-salzburg/j.php?MTID=mcc4d135f9c27bc7ab9207328bc913e65
Abstract: In the talk we consider regular polytopes in n-dimensional lattices: the n-dimensional cube, the n-dimensional pyramid and the n-dimensional simplex. It turns out that the number of lattice points on the surfaces of these objects can be described by certain polynomials fn, gn, hn, respectively. We study the Diophantine equations F(x)=G(y), where F is one of fn, gn, hn, and G is a polynomial with rational coefficients, proving various effective and ineffective finiteness theorems. Our results are closely related to those of Bazsó, Bennett, Bilu, Gyõry, Hajdu, Pethõ, Pintér, Tengely, Tichy, Tijdeman, Varga and many others. The presented new results are joint with L. Hajdu.