Abelian Functions for Trigonal Curves of Genus Three
Abstract
We develop the theory of generalized Weierstrass sigma- and -functions defined on a trigonal curve of genus three. In particular we give a list of the associated partial differential equations satisfied by the -functions, a proof that the coefficients of the power series expansion of the sigma-function are polynomials of moduli parameters, and the derivation of two addition formulae.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.