symplectic matrices - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-20T18:32:02Z http://mathoverflow.net/feeds/question/40662 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/40662/symplectic-matrices symplectic matrices Robert Gunning 2010-09-30T19:23:49Z 2011-03-05T20:35:03Z <p>If $( A B | C D)$ is a symplectic matrix with entries in the finite field with two elements, is it necessarily the case that $\sum_{i,j,k} a_{ij}b_{ij}c_{ik}d_{ik} = 0$?</p> <p>This arose in connection with some calculations involving theta functions. There seems to be some indication that it might be true, and I could not come up with a counterexample; but experts in the area may well know the answer right off. </p> <p>Thanks for any help.</p>