Effective Theorems for Quadratic Spaces Over Q-bar

Document Type



Mathematics (CMC)

Publication Date



Let N >=2 be an integer, F a quadratic form in N variables over Qbar, and Z contained in Qbar^N an L-dimensional subspace, 1 <= L <= N. We prove the existence of a small-height maximal totally isotropic subspace of the bilinear space (Z,F). This provides an analogue over Qbar of a well-known theorem of Vaaler proved over number fields. We use our result to prove an effective version of Witt decomposition for a bilinear space over Qbar. If time allows, we will also discuss some related effective results on orthogonal decomposition and structure of isometries for a bilinear space over Qbar. This extends previous results of the author over number fields. All bounds on height are explicit.


This lecture was given during the Number Theory Seminar at Texas A&M University in January 2006.

Rights Information

© 2006 Lenny Fukshansky

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.