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    27.08.2015 - 27.08.2015

    Invitation to the special lectures

    Department of Mathematics, FoS, invites to lectures from foreign experts.

    8:00-8:45 Prof. Diego Marques, University of Brasilia, Brazil,
     
               On the mithmetic behavior of transcendental functions
     
     
    9:00-9:45 Prof. Yuri Sachkov,  Program Systems Institute of Russian
               Academy of Sciences Pereslavl-Zalessky, Russia
     

    Diego Marques - Professor of the Department of Mathematics at University of Brasilia, Brazil. He got PhD in Mathematics from the same university in 2009. His research focuses on Number Theory: transcendental number theory, Diophantine approximation, Diophantine equations and recurrence sequences.

    Abstract: The study of the arithmetic behavior of transcendental functions at complex points has attracted the attention of many mathematicians for decades. The first result concerning this subject goes back to 1884, when Lindemann proved that the transcendental function e^z assumes transcendental values at all nonzero algebraic point. In 1886, Strauss tried to prove that an analytic transcendental function cannot be rational at all rational points in its domain. However, in 1886, Weierstrass supplied him with a counter-example and also stated (without proof) that there are transcendental entire functions which assume algebraic values at all algebraic points. This assertion was proved in 1895 by Stäckel who established a much more general result. Subsequent advances were made by Stäckel, Faber, Mahler, Van der Poorten, etc. In particular, Mahler (in his 1976 book and in a 1984 paper) raised some questions about this subject.

     

    In this talk, we shall provide a brief overview of the classical results in this field as well as our advances related to these Mahler's questions (in particular, the solution for two of them). This is related to joint works with Moreira, Ramirez and Schleischitz.



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Last modified:  Vávrová Kristýna, 18.12.2017 14:45