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Small zeros of quadratic forms over number fields. II
| Content Provider | Semantic Scholar |
|---|---|
| Author | Vaaler, Jeffrey D. |
| Copyright Year | 1987 |
| Abstract | Let F be a nontrivial quadratic form in N variables with coefficients in a number field k and let A be a K x N matrix over k. We show that if the simultaneous equations F(x) = 0 and Ax = 0 hold on a subspace X of dimension L and L is maximal, then such a subspace X can be found with the height of X relatively small. In particular, the height of 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 adele spaces and local to global techniques which generalize recent work of H. P. Schlickewei. |
| Starting Page | 281 |
| Ending Page | 296 |
| Page Count | 16 |
| File Format | PDF HTM / HTML |
| DOI | 10.1090/S0002-9947-1987-0887510-6 |
| Volume Number | 302 |
| Alternate Webpage(s) | http://www.ams.org/journals/tran/1989-313-02/S0002-9947-1989-0940914-7/S0002-9947-1989-0940914-7.pdf |
| Alternate Webpage(s) | http://www.ams.org/journals/tran/1987-302-01/S0002-9947-1987-0887510-6/S0002-9947-1987-0887510-6.pdf |
| Alternate Webpage(s) | https://doi.org/10.1090/S0002-9947-1987-0887510-6 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
