On the number of real critical points of logarithmic derivatives and the Hawaii conjecture
نویسندگان
چکیده
For a given real entire function φ with finitely many nonreal zeros, we establish a connection between the number of real zeros of the functions Q = (φ/φ) and Q1 = (φ /φ). This connection leads to a proof of the Hawaii conjecture [T.Craven, G.Csordas, and W. Smith, The zeros of derivatives of entire functions and the Pólya-Wiman conjecture, Ann. of Math. (2) 125 (1987), 405–431] stating that the number of real zeros of Q does not exceed the number of nonreal zeros of φ.
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