I4406 - Diophantine Number Theory

In this joint project of the FWF and the NKFIH we shall use different techniques from Diophantine number theory (as the subspace theorem, the theory of linear forms in logarithms, Runge's method, hypergeometric methods, etc.) to study various Diophantine problems. E.g. we work on Ritt's decomposition theory and Diophantine applications, we shall study some classical Diophantine equations (as the ErdÃ¶s-Straus conjecture, Goormaghtigh's equation and the generalized Ramanujan-Nagell equation, Thue and relative Thue equations), and we shall investigate Diphantine problems with recurrence sequences. We emphasize that the Austrian and Hungarian research groups have a long standing and very fruitful cooperation, which is exceptional even by the international standards. Through this project we want to maintain this tight scientific bond and in particular encourage collaboration between younger members of the groups.

In this joint project of the FWF and the NKFIH we shall use different techniques from Diophantine number theory (as the subspace theorem, the theory of linear forms in logarithms, Runge's method, hypergeometric methods, etc.) to study various Diophantine problems. E.g. we work on Ritt's decomposition theory and Diophantine applications, we shall study some classical Diophantine equations (as the ErdÃ¶s-Straus conjecture, Goormaghtigh's equation and the generalized Ramanujan-Nagell equation, Thue and relative Thue equations), and we shall investigate Diphantine problems with recurrence sequences. We emphasize that the Austrian and Hungarian research groups have a long standing and very fruitful cooperation, which is exceptional even by the international standards. Through this project we want to maintain this tight scientific bond and in particular encourage collaboration between younger members of the groups.

The project has started on 01.04.2020.

Team:

Clemens Fuchs (Salzburg; co-PI)

Kalman Gyõry (Debrecen; PI)

Lajos Hajdu (Debrecen; co-PI)

Sebastian Heintze (Salzburg)

Robert Tichy (Graz; PI)

Ingrid Vukusic (Salzburg; funded by FWF-I4406)

Volker Ziegler (Salzburg)

Clemens Fuchs (Salzburg; co-PI)

Kalman Gyõry (Debrecen; PI)

Lajos Hajdu (Debrecen; co-PI)

Sebastian Heintze (Salzburg)

Robert Tichy (Graz; PI)

Ingrid Vukusic (Salzburg; funded by FWF-I4406)

Volker Ziegler (Salzburg)

TBA

C. Fuchs, S. Heintze: A polynomial variant of Diophantine triples in linear recurrences, arXiv:2006.12173

C. Fuchs, S. Heintze: Norm form equations with solutions taking values in a multi-recurrence, arXiv:2006.11075

C. Fuchs, S. Heintze: On the growth of linear recurrences in function fields, arXiv:2006.11074

C. Fuchs, S. Heintze: Another S-unit variant of Diophantine tuples, PAMS, to appear, arXiv:1910.09285

TBA

TBA

Impressum 23.06.2020