Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

On Three Rational Functions on a Riemann Surface


Affiliations
1 Madras University, India
     

   Subscribe/Renew Journal


Let y be an algebraic function of z defined by the irreducible relation

F(y, z)=A0(z)yn+A1(z)yn-1+...+ An(z) = 0                     (1)

where the A's are polynomials in z of degree, say, m. The manifold of pairs of values y, z which satisfy the given equation (1) constitute the Riemann surface of the algebraic function y, constructed in the usual manner. Any rational function of y and s is a rational function of position on this Riemann surface. The order of such a rational function is the number of places on the surface at which it takes an assigned value. In particular, y and z are rational functions of position on the surface of orders m and n respectively.


Subscription Login to verify subscription
User
Notifications
Font Size


Abstract Views: 188

PDF Views: 0




  • On Three Rational Functions on a Riemann Surface

Abstract Views: 188  |  PDF Views: 0

Authors

K. S. Suryanarayan
Madras University, India

Abstract


Let y be an algebraic function of z defined by the irreducible relation

F(y, z)=A0(z)yn+A1(z)yn-1+...+ An(z) = 0                     (1)

where the A's are polynomials in z of degree, say, m. The manifold of pairs of values y, z which satisfy the given equation (1) constitute the Riemann surface of the algebraic function y, constructed in the usual manner. Any rational function of y and s is a rational function of position on this Riemann surface. The order of such a rational function is the number of places on the surface at which it takes an assigned value. In particular, y and z are rational functions of position on the surface of orders m and n respectively.