On the growth of multi-recurrences

Clemens Fuchs; Sebastian Heintze

doi:10.1007/s00013-022-01775-5

On the growth of multi-recurrences

Arch Math. 2022;119(5):489-494. doi: 10.1007/s00013-022-01775-5. Epub 2022 Sep 27.

Authors

Clemens Fuchs¹, Sebastian Heintze²

Affiliations

¹ Department of Mathematics, University of Salzburg, Hellbrunnerstr. 34, 5020 Salzburg, Austria.
² Institute of Analysis and Number Theory, Graz University of Technology, Steyrergasse 30/II, 8010 Graz, Austria.

Abstract

In this paper, we provide a complete proof for a bound on the growth of multi-recurrences which are defined over a number field. The proven bound was already stated by van der Poorten and Schlickewei 40 years ago.

Keywords: Growth; Multi-recurrence; S-units.