Mathematics by Somos

To have a real understanding of mathematics you have to know its history and MacTutor History of Mathematics is a good place to find it.

Meanwhile, many places on the web have mathematical content. A particularly good place to find mathematical reference information is the MathWorld by Eric Weisstein. For sequences of integers, the place to go for information is the On-Line Encyclopedia of Integer Sequences (OEIS) originated by Neil Sloane where I have authored over 1900 sequences.

I am interested in algebraic identities and for my own use I have collected over 500 of them which have a simple, special form. They are used in proving theorems and, more importantly, some have associated functional equations which characterise somos elliptic functions. My list of Special Algebraic Identities (257kB) is here.

I am interested in Combinatorics and Discrete Mathematica and this includes graph theary. For my own use I transcribed an almost exact copy of a short 1881 article by Arthur Cayley titled "On the Analytical Forms Called Trees". I have links to both PDF form and LaTeX form.

The Elliptic Realm

Much of my work since the 1980s is associated with the Elliptic Realm. A recent example is an essay "A Multisection of q-Series" (30Jan2017) (PDF,DVI,text,LaTeX) -- a brief introduction in the style of Ramanujan, rediscovering two of his continued fractions and Klein's quartic curve. I have been working on Weierstrass Elliptic Function Polynomials (wxyz.gp) which is a PARI/GP program with a lot of polynomial sequence identities. The Mathematica version (wxyz.wl) is here also. I have been interested in Monstrous Moonshine since the 1980s. I have many results related to the replicable functions and modular functions associated with the topic. I have PARI/GP replicable function code. Contact me if you want a copy of my results.

A small part of my work resulted in an essay "A Remarkable eta-product Identity" (23Mar2010) (PDF,DVI,text,LaTeX) on one of thousands of eta-product identities collected at my Dedekind eta function product identities website. Another small part of my work is an essay "Rational Function Multiplicative Coefficients" (21Feb2011) (PDF,DVI,text,LaTeX) on two related conjectures on rational functions with multiplicative coefficients.

Also see


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Last Updated Thu Apr 06 2017
Michael Somos <ms639@georgetown.edu>
Michael Somos "http://somos.crg4.com/"