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Proceedings of the American Mathematical Society

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Fourier transforms with only real zeros

Author: Charles M. Newman
Journal: Proc. Amer. Math. Soc. 61 (1976), 245-251
MSC: Primary 10H05; Secondary 42A68
MathSciNet review: 0434982
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Abstract: The class of even, nonnegative, finite measures $ \rho $ on the real line such that for any $ b > 0$ the Fourier transform of $ \exp ( - b{t^2})d\rho (t)$ has only real zeros is completely determined. This result is then applied to the Riemann hypothesis.

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