Digital Library of Mathematical Functions
About the Project
NIST
21 Multidimensional Theta FunctionsApplications

§21.8 Abelian Functions

An Abelian function is a 2g-fold periodic, meromorphic function of g complex variables. In consequence, Abelian functions are generalizations of elliptic functions (§23.2(iii)) to more than one complex variable. For every Abelian function, there is a positive integer n, such that the Abelian function can be expressed as a ratio of linear combinations of products with n factors of Riemann theta functions with characteristics that share a common period lattice. For further information see Igusa (1972, pp. 132–135) and Markushevich (1992).