Improvements in Birch’s theorem on forms in many variables
| Autor: | Tim D Browning, Sean Prendiville |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Degree (graph theory)
Mathematics::Number Theory Applied Mathematics General Mathematics 010102 general mathematics Integral form 01 natural sciences 11P55 (11G35 14G05) Combinatorics math.NT Birch's theorem If and only if TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY 0103 physical sciences 010307 mathematical physics 0101 mathematics Mathematics |
| Zdroj: | Browning, T D & Prendiville, S M 2017, ' Improvements in Birch's theorem on forms in many variables ', Journal für die reine und angewandte Mathematik, vol. 2017, no. 731, pp. 203-234 . https://doi.org/10.1515/crelle-2014-0122 |
| ISSN: | 1435-5345 0075-4102 |
| DOI: | 10.1515/crelle-2014-0122 |
| Popis: | We show that a non-singular integral form of degree d is soluble over the integers if and only if it is soluble over ℝ {\mathbb{R}} and over ℚ p {\mathbb{Q}_{p}} for all primes p, provided that the form has at least ( d - 1 2 d ) 2 d {(d-\frac{1}{2}\sqrt{d})2^{d}} variables. This improves on a longstanding result of Birch. |
| Databáze: | OpenAIRE |
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