J. Austral. Math. Soc.
72 (2002), 87-91
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About a problem of Hermite and Biehler
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Abstract
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A point of departure for this paper is the
famous theorem of Hermite and Biehler: If
f(z) is a polynomial with complex coefficients
ak and its zeros zk
satisfy Im zk > 0,
then the polynomials with coefficients Re ak
and Im ak
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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