Diophantine approximation for products of linear maps -- logarithmic improvements
| Autor: | Pankaj Vishe, Alexander Gorodnik |
|---|---|
| Přispěvatelé: | University of Zurich |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Logarithm
Applied Mathematics General Mathematics 010102 general mathematics Multiplicative function Mathematical analysis Zero (complex analysis) Diophantine approximation 01 natural sciences 10123 Institute of Mathematics math.NT 510 Mathematics 2604 Applied Mathematics Product (mathematics) 0103 physical sciences Applied mathematics 010307 mathematical physics Affine transformation 0101 mathematics Abelian group math.DS Mathematics 2600 General Mathematics |
| Zdroj: | Gorodnik, A & Vishe, P 2018, ' Diophantine approximation for products of linear maps--logarithmic improvements ', Transactions of the American Mathematical Society, vol. 370, no. 1, pp. 487-507 . https://doi.org/10.1090/tran/6953 Transactions of the American Mathematical Society, 2016, Vol.370(1), pp.487-507 [Peer Reviewed Journal] |
| Popis: | This paper is devoted to the study of a problem of Cassels in multiplicative Diophantine approximation which involves minimising values of a product of affine linear forms computed at integral points. It was previously known that values of this product become arbitrary close to zero, and we establish that, in fact, they approximate zero with an explicit rate. Our approach is based on investigating quantitative density of orbits of higher-rank abelian groups. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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