Mathematics by Somos

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 660 of them which have a simple, special form. They are used in proving theorems and, more importantly, some have associated functional equations which characterise some elliptic functions. My list of Special Algebraic Identities is here.

I am interested in Combinatorics and Discrete Mathematics and this includes graph theory. For my own use I have 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 Math Project) with a lot of polynomial sequence identities. The PARI/GP version (, and The Wolfram language 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 former Dedekind eta function product identities website. That website last version is saved at the Wayback Machine. 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 Jan 14 2022
Michael Somos <>
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