Journal d'Analyse Mathématique

, Volume 117, Issue 1, pp 87–118 | Cite as

Non-real zeroes of real entire derivatives

Article

Abstract

A real entire function belongs to the Laguerre-Pólya class LP if it is the limit of a sequence of real polynomials with real zeroes. By building upon results that resolved a long-standing conjecture of Wiman, a number of conditions are established under which a real entire function f must belong to the class LP, or to one of the related classes U2p*. These conditions typically involve the non-real zeroes of f and its derivatives, or those of the differential polynomial f f″−a(f′)2.

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Copyright information

© Hebrew University Magnes Press 2012

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of NottinghamNottinghamUK

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