I am interested in computers, mathematics, and particularly number sequences. My specialties are Ramanujan theta functions and Lambert series, modular forms and functions, elliptic functions and curves, multilinear recurrence relations, enumerative combinatorics and continued fraction expansions.

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 2000 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 (270KB) 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.

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

- Number Walls in Combinatorics (PDF,LaTeX).
- Grossman's constant recurrence sequence research results.
- The Origin of Elliptic Functions.
- In the Elliptic Realm.
- Gale-Robinson Polynomials.
- Somos Polynomials.
- Somos 6 Sequence.
- Somos 7 Sequence.
- Rational Triangles.
- Heronian triangles.
- Pythagorean triples.

Back to my home page

Michael Somos <ms639@georgetown.edu>

Michael Somos