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.
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Translated from Matematicheskie Zametki, Vol. 17, No. 4, pp. 525–529, April, 1975.
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Gol'dberg, A.A. Nevanlinna's lemma on the logarithmic derivative of a meromorphic function. Mathematical Notes of the Academy of Sciences of the USSR 17, 310–312 (1975). https://doi.org/10.1007/BF01105380
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DOI: https://doi.org/10.1007/BF01105380