Unity Root Matrix Theory - arXiv endorser?
richard miller
entitled "Unity Root Matrix Theory". The usual method is to search on
arXiv and I have done so. My problem is that the paper is a complete
mishmash of mathematical physics, number theory and linear algebra. It
could be all of them and none of them. The title is a bit too specific
but the best I could think of.
Abstract below with classification codes. Note the Pythag triples
apsect is another paper for which I have found a few appropriate arXiv
authors, but a few more would not go amiss.
email reply: ric...@microscitech.com
Richard Miller
Abstract
This paper studies a conservation equation and its solution in
integers. The conservation equation is formulated in terms of
dynamical variables, called ‘unity roots’, also known as primitive
roots of unity in number theory, which are the integer equivalents to
the complex roots of unity. The dynamical equations and their
solutions are subsequently derived from the conservation equation by
imposition of an invariance principle on the unity roots linking them
with the familiar , and coordinates. The dynamical equations are
expressible in matrix form with the unity roots as elements and the
coordinate solution as a particular eigenvector. Extensions to higher
order show this solution to be that of an nth order Diophantine
equation and, consequently, a correspondence is established between
the space of dynamical variables and that of the coordinates.
Simplifications reduce the Diophantine equation to the familiar
Pythagoras equation, with Pythagorean triples as eigenvectors of the
dynamical equations and new Pythagorean relations subsequently
obtained.
Keywords. Integer Matrix, Variational methods, Primitive Root,
Diophantine Equation, Pythagorean Triple.
MSC2010 Mathematical Subject Classification. 11A15, 11C20, 11D41,
15A18, 15B36, 70H30