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{\bf Using squares of real-valued functions to prove that
the $\Xi^*(z)$ function\\
and certain other entire functions have only real zeros\\}
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George Gasper, Northwestern University, U.S.A. \\
Email: george@math.nwu.edu\\
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{\bf Abstract}

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It is shown how squares of real-valued functions can be used to give new
proofs of the reality of the zeros of

$$ \Xi^*(z) = 4\pi^2 \int_0^\infty \cosh \frac{9}{2}u \ e^{-2\pi \cosh 2u} \cos zu \ du,$$

$$  K_{iz}(a) = \int_0^\infty  e^{-a \cosh u} \cos zu \  du, \ \ a > 0,$$
and of some other entire functions.

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