Combinatorical and Algebraic Structures Seminar
Session details
| Date: | 29.3.2011 |
| Speaker: | Tomáš Hejda, FJFI, České vysoké učení technické v Praze |
| Title: | On one cruel diophantic equation in M\"obius number systems |
| Abstract: | We study number systems generated by M\"obius transformations (MT) of the hyperbolic plane $\mathbb{U}=\{z\in\mathbb C|\Im z\geq0\}$. We are concerned about finitely generated groups of MTs that are discrete in the group of all MTs. Any MT is a map $z\rightarrow\frac{az+b}{cz+b}$ with parameters $a,b,c,d\in\mathbb R$ and $ad-bc>0$. We want to prove that no system of purely rational MTs exist such that it generates a redundant number system. It is equivanent to showing that some system of diophantic equations in \emph{eight} variables has no solution. We would like to ask the auditorium for some ideas how to prove this. |
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