Notes on theta functions for open Riemann surfaces

Notes on Compact Riemann Surfaces

Computing Riemann theta functions

The Riemann theta function is a complex-valued function of g complex variables. It appears in the construction of many (quasi-)periodic solutions of various equations of mathematical physics. In this paper, algorithms for its computation are given. First, a formula is derived allowing the pointwise approximation of Riemann theta functions, with arbitrary, user-specified precision. This formula ...

Riemann Surfaces and Theta Functions MAST 661G / MAST 837J

Ideal Theory on Open Riemann Surfaces

Introduction. The theorems of the classical ideal theory in fields of algebraic numbers hold in rings of analytic functions on compact Riemann surfaces. The surfaces admitted in our discussion are closely related to algebraic surfaces; we deal either with compact surfaces from which a finite number of points are omitted or, more generally, with surfaces determined by an algebroid function. The ...

Meromorphic Functions on Certain Riemann Surfaces

1. Throughout the paper we shall denote by R a Riemann surface. For a domain Í2 in P, we represent by AB(Q) the class of all the singlevalued bounded analytic functions on the closure Ü. For a meromorphic function / on a domain ß, we use the notation viw\f, Q.) to express the number of times that/ attains w in ß. Definition 1. We say that REWIb if the maximum principle suplen \fip)\ =sup3,ean \...