Loading...
Please wait, while we are loading the content...
Similar Documents
Small Zeros of Quadratic Forms Over Number Fields
| Content Provider | Scilit |
|---|---|
| Author | Vaaler, Jeffrey D. |
| Copyright Year | 1987 |
| Description | Let $F$ be a nontrivial quadratic form in $N$ variables with coefficients in a number field $k$ and let $A$ be a $K \times N$ matrix over $k$. We show that if the simultaneous equations $F({\mathbf {x}}) = 0$ and $A{\mathbf {x}} = 0$ hold on a subspace $\mathfrak {X}$ of dimension $L$ and $L$ is maximal, then such a subspace $\mathfrak {X}$ can be found with the height of $\mathfrak {X}$ relatively small. In particular, the height of $\mathfrak {X}$ can be explicitly bounded by an expression depending on the height of $F$ and the height of $A$. We use methods from geometry of numbers over adèle spaces and local to global techniques which generalize recent work of H. P. Schlickewei. |
| Related Links | https://www.ams.org/tran/1987-302-01/S0002-9947-1987-0887510-6/S0002-9947-1987-0887510-6.pdf |
| Ending Page | 296 |
| Page Count | 16 |
| Starting Page | 281 |
| ISSN | 00029947 |
| e-ISSN | 10886850 |
| DOI | 10.2307/2000910 |
| Journal | Transactions of the American Mathematical Society |
| Issue Number | 1 |
| Volume Number | 302 |
| Language | English |
| Publisher | Duke University Press |
| Publisher Date | 1987-07-01 |
| Access Restriction | Open |
| Subject Keyword | Mathematical Physics Quadratic Form Number Fields Mathbf Subspace Simultaneous Hold Nontrivial Maximal Explicitly |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics |
