A Quaternionic Proof of the Universality of Some Quadratic Forms

Details A Quaternionic Proof of the Universality of Some Quadratic Forms A Quaternionic Proof of the Universality of Some Quadratic Forms

2004-06-22

arxiv.org/abs/math/0406429v1

Mathematics

Number Theory

Approx. 20 pages. Submitted in revised form to the Journal of Number Theory

Scientific paper

Quadratic forms over Z that represent all positive integers are called universal. Starting with Ramanujan, 54 universal quaternary quadratic forms without cross product terms were discovered. The form that is the sum of four squares was proved universal by Hurwitz using a special ring of quaternions. Here seven other quaternary quadratic forms are shown universal by investigation of appropriate rings of quaternions.

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