تقرير
Mahler's work on Diophantine equations and subsequent developments
| العنوان: | Mahler's work on Diophantine equations and subsequent developments |
|---|---|
| المؤلفون: | Evertse, Jan-Hendrik, Győry, Kálmán, Stewart, Cameron L. |
| المصدر: | Documenta Mathematica, Extra Vol., Mahler Selecta (2019), 149-171 |
| سنة النشر: | 2018 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - History and Overview, Mathematics - Number Theory, 11D25, 11D45, 11D57, 11D59, 11D61, 11J61, 11J68 |
| الوصف: | We discuss Mahler's work on Diophantine approximation and its applications to Diophantine equations, in particular Thue-Mahler equations, S-unit equations and S-integral points on elliptic curves, and go into later developments concerning the number of solutions to Thue-Mahler equations and effective finiteness results for Thue-Mahler equations. For the latter we need estimates for p-adic logarithmic forms, which may be viewed as an outgrowth of Mahler's work on the p-adic Gel'fond-Schneider theorem. We also go briefly into decomposable form equations, these are certain higher dimensional generalizations of Thue-Mahler equations. Comment: 26 pages. This paper will appear in "Mahler Selecta", a volume dedicated to the work of Kurt Mahler and its impact |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1806.00355 |
| رقم الأكسشن: | edsarx.1806.00355 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |