On the Number of Nonreal Zeros of Real Entire Functions and the Fourier-pólya Conjecture Haseo Ki

  title={On the Number of Nonreal Zeros of Real Entire Functions and the Fourier-p{\'o}lya Conjecture Haseo Ki},
  author={Haseo Ki and Young-One Kim},
This paper is concerned with a general theorem on the number of nonreal zeros of transcendental functions. J. Fourier formulated the theorem in his work Analyse des équations déterminées in 1831, but he did not give a proof. Roughly speaking, the theorem states that if a real entire function f (x) can be expressed as a product of linear factors, then we can count the nonreal zeros of f (x) by observing the behavior of the derivatives of (x) on the real axis alone. As we shall see in the sequel… CONTINUE READING

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