1898/12/31 by E. T. Whittaker · 2 citations
Mathematics · #Advanced Differential Equations and Dynamical Systems #Mathematics and Applications #Advanced Topics in Algebra
paper · pdf · doi:10.1098/rspl.1898.0033
openalex publication_date 1898/12/31 · openalex created_date 2016/06/24 · openalex updated_date 2026/05/21
Abstract If u and z are variables connected by an algebraic equation, they are, in general, multiform functions of each other; the multiformity can be represented by a Riemann surface, to each point of which corresponds a pair of values of u and z. Poincaré and Klein have proved that a variable t exists, of which u and z are uniform automorphic functions; the existence-theorem, however, does not connect t analytically with u and z. When the genus (genre, Geschlecht) of the algebraic relation is zero oi unity, t can be found by known methods; the automorphic functions required are rational functions, and doubly periodic functions, in the two case respectively.