Ramification and unintegrated value distribution

John Robert Quine, Jr.

Vol. 122 (1986), No. 2, 441–447

DOI: 10.2140/pjm.1986.122.441

Abstract

For a holomorphic map f from the complex plane into the Riemann sphere, the ramification term n₁(f,r) is studied. A geometric version of ramification is defined in terms of the intersection points of f(z) × f(z + h) with the diagonal Δ for a suitable vector field h. Estimates of a counting function for this intersection number are given in terms of the mean covering number.

Mathematical Subject Classification 2000

Primary: 30D35

Milestones

Received: 28 June 1984

Published: 1 April 1986