J. Austral. Math. Soc.
72 (2002), 8791

About a problem of Hermite and Biehler


Abstract

A point of departure for this paper is the
famous theorem of Hermite and Biehler: If
f(z) is a polynomial with complex coefficients
a_{k} and its zeros z_{k}
satisfy Im z_{k} > 0,
then the polynomials with coefficients Re a_{k}
and Im a_{k}
have only real zeros. We generalize this
theorem for some entire functions. The entire
functions in Theorem 2 and Theorem 3 are of first and second genus
respectively.

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