Article

Numerical Algorithms

, Volume 25, Issue 1, pp 109-122

Conjectures and theorems in the theory of entire functions

  • George CsordasAffiliated withDepartment of Mathematics, University of Hawaii
  • , Dimitar K. DimitrovAffiliated withDCCE, IBILCE, UNESP

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Abstract

Motivated by the recent solution of Karlin's conjecture, properties of functions in the Laguerre–Pólya class are investigated. The main result of this paper establishes new moment inequalities for a class of entire functions represented by Fourier transforms. The paper concludes with several conjectures and open problems involving the Laguerre–Pólya class and the Riemann ξ-function.

Laguerre–Pólya class Karlin's conjecture Turán inequalities double Turán inequalities Fourier transform admissible kernel Riemann hypothesis de Bruijn–Newman constant