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On Equilibrium Points of Logarithmic and Newtonian Potentials
Author(s) -
Clunie J.,
Eremenko A.,
Rossi J.
Publication year - 1993
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-47.2.309
Subject(s) - logarithm , meromorphic function , logarithmic derivative , newtonian potential , distribution (mathematics) , derivative (finance) , function (biology) , conjugate , conjugate points , mathematics , physics , mathematical physics , mathematical analysis , quantum mechanics , gravitation , evolutionary biology , financial economics , economics , biology
Let f ( z ) =∑ j − 1 ∞a j / ( z − z j )and∑ j − 1 ∞ | a j | / | z j | < ∞ . Then f can be realized as the complex conjugate of the gradient of a logarithmic potential or, for integral a j , as the logarithmic derivative of a meromorphic function. We investigate conditions on a j and z j that guarantee that f has zeros. In the potential theoretic setting, this asks whether certain logarithmic potentials with discrete mass distribution have equilibrium points.