Minimal rank of universal lattices and number of indecomposable elements in real multiquadratic fields.(English)Zbl 1550.11052
Author’s abstract: We establish an upper bound on the number of real multiquadratic fields that admit a universal quadratic lattice of a given rank, or contain a given amount of indecomposable elements modulo totally positive units, obtaining density zero statements. We also study the structure of indecomposable elements in real biquadratic fields, and compute a system of indecomposable elements modulo totally positive units for some families of real biquadratic fields.
Reviewer: Meinhard Peters (Münster)
MSC:
| 11E12 | Quadratic forms over global rings and fields |
| 11E20 | General ternary and quaternary quadratic forms; forms of more than two variables |
| 11H55 | Quadratic forms (reduction theory, extreme forms, etc.) |
| 11R20 | Other abelian and metabelian extensions |
| 11R80 | Totally real fields |
| 11A55 | Continued fractions |
Cite
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