تقرير
Partition regularity of generalized Pythagorean pairs
| العنوان: | Partition regularity of generalized Pythagorean pairs |
|---|---|
| المؤلفون: | Frantzikinakis, Nikos, Klurman, Oleksiy, Moreira, Joel |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, Mathematics - Number Theory, Primary: 05D10, Secondary:11N37, 11B30, 37A44 |
| الوصف: | We address partition regularity problems for homogeneous quadratic equations. A consequence of our main results is that, under natural conditions on the coefficients $a,b,c$, for any finite coloring of the positive integers, there exists a solution to $ax^2+by^2=cz^2$ where $x$ and $y$ have the same color (and similar results for $x,z$ and $y,z$). For certain choices of $(a,b,c)$, our result is conditional on an Elliott-type conjecture. Our proofs build on and extend previous arguments of the authors dealing with the Pythagorean equation. We make use of new uniformity properties of aperiodic multiplicative functions and concentration estimates for multiplicative functions along arbitrary binary quadratic forms. Comment: 49 pages. Small changes made |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.08360 |
| رقم الأكسشن: | edsarx.2407.08360 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |