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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Fourier transforms with only real zeros
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by Charles M. Newman PDF
Proc. Amer. Math. Soc. 61 (1976), 245-251 Request permission

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.
References
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 61 (1976), 245-251
  • MSC: Primary 10H05; Secondary 42A68
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0434982-5
  • MathSciNet review: 0434982