Sums of squares and orthogonal integral vectors

Details Sums of squares and orthogonal integral vectors Sums of squares and orthogonal integral vectors

2008-06-24

arxiv.org/abs/0806.3943v2

Mathematics

Number Theory

23 pages, final version to appear in Journal of Number Theory

Scientific paper

Two vectors in $\BZ^3$ are called \emph{twins} if they are orthogonal and have the same length. The paper describes twin pairs using cubic lattices, and counts the number of twin pairs with a given length. Integers $M$ with the property that each integral vector with length $\sqrt{M}$ has a twin are called twin-complete. They are completely characterized modulo a famous conjecture in number theory. The main tool is the decomposition theory of Hurwitz integral quaternions. Throughout the paper we made a concerted effort to keep the exposition as elementary as possible.

Affiliated with

Also associated with

No associations

Rating

Sums of squares and orthogonal integral vectors does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Sums of squares and orthogonal integral vectors, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Sums of squares and orthogonal integral vectors will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-98114