arXiv subjects

Jesse I. Deutsch

Publications and source records attributed to Jesse I. Deutsch.

2 recordsLinked to original sources

arXiv2004

A Quaternionic Proof of the Universality of Some Quadratic Forms

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.

math.NT↗

arXiv2004

A Quaternionic Proof of the Representation Formula of a Quaternary Quadratic Form

Recently the author used certain quaternion orders to demonstrate the universality of some quaternary quadratic forms. Here a further study is done on one of these orders analogous to Hurwitz's proof of the formula for the number of representations of a positive integer by sums of four squares using quaternions. The result is the formula for the number of representations of a positive integer by one of the above mentioned quaternary quadratic forms.

math.NT↗