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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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


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.
  • N. G. de Bruijn, The roots of trigonometric integrals, Duke Math. J. 17 (1950), 197–226. MR 37351
  • Morris Marden, The Geometry of the Zeros of a Polynomial in a Complex Variable, Mathematical Surveys, No. 3, American Mathematical Society, New York, N. Y., 1949. MR 0031114
  • Charles M. Newman, Zeros of the partition function for generalized Ising systems, Comm. Pure Appl. Math. 27 (1974), 143–159. MR 484184, DOI 10.1002/cpa.3160270203
  • Charles M. Newman, Inequalities for Ising models and field theories which obey the Lee-Yang theorem, Comm. Math. Phys. 41 (1975), 1–9. MR 376061
  • Charles M. Newman, Classifying general Ising models, Les méthodes mathématiques de la théorie quantique des champs (Colloq. Internat. CNRS, No. 248, Marseille, 1975) Éditions Centre Nat. Recherche Sci., Paris, 1976, pp. 273–288 (English, with French summary). MR 0479247
  • George Pólya, Collected papers, Mathematicians of Our Time, Vol. 7, MIT Press, Cambridge, Mass.-London, 1974. Vol. 1: Singularities of analytic functions; Edited by R. P. Boas. MR 0505093
  • Barry Simon and Robert B. Griffiths, The $(\phi ^{4})_{2}$ field theory as a classical Ising model, Comm. Math. Phys. 33 (1973), 145–164. MR 428998
  • E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, Oxford, at the Clarendon Press, 1951. MR 0046485
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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:
  • MathSciNet review: 0434982