A local estimate for typically real functions

George Berry Leeman, Jr.

Vol. 52 (1974), No. 2, 481–484

DOI: 10.2140/pjm.1974.52.481

Abstract

In this paper it is shown that for each typically real function f(z) = z + ∑ _n=2^∞a_nzⁿ the local estimate n−a_n ≦ (1∕6)n(n² − 1)(2 −a₂) holds, n = 2,3,⋯ . The constant (1∕6)n(n² − 1) is best possible.

Mathematical Subject Classification

Primary: 30A34

Milestones

Received: 29 June 1973

Published: 1 June 1974