This article is cited in 7 papers

Nevanlinna's lemma on the logarithmic derivative of a meromorphic function

A. A. Gol'dberg

L'vov State University

Abstract: In proving the second fundamental theorem for functions meromorphic in the half-plane, Nevanlinna has asserted (in 1925) that they satisfy a lemma similar to the well-known lemma on the logarithmic derivative, but his proof was based on additional assumptions. These assumptions were later relaxed by Dufresnoy (in 1939) and Ostrovskii (in 1961). Here we shall show that in the general case, functions which are meromorphic in the half-plane do not satisfy a lemma similar to the lemma on the logarithmic derivative.

UDC: 517.535.4

Received: 18.02.1974

 English version: Mathematical Notes, 1974, 17:4, 310–312

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