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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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The values of exponential polynomials at algebraic points. I
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by Carlos Julio Moreno PDF
Trans. Amer. Math. Soc. 186 (1973), 17-31 Request permission

Abstract:

A strengthening of Siegel’s proof of the Hermite-Lindemann Theorem is given. The results are used to obtain lower bounds for the values of exponential polynomials at algebraic points. The question of how well the root of an exponential polynomial can be approximated by algebraic numbers is considered, and a lower bound is obtained for the absolute value of the difference between a root of the exponential polynomial and an algebraic number.
References
  • N. I. Fel′dman, Arithmetic properties of the solutions of a transcendental equation, Vestnik Moskov. Univ. Ser. I Mat. Meh. 1964 (1964), no. 1, 13–20 (Russian, with English summary). MR 0158869
  • A. O. Gel′fond, Transcendental and algebraic numbers, Dover Publications, Inc., New York, 1960. Translated from the first Russian edition by Leo F. Boron. MR 0111736
    • C. Hermite, Sur la fonction exponentielle, Acad. Sci. Paris 77 (1873); Ouvres. III, 150-181.
  • Serge Lang, Introduction to transcendental numbers, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1966. MR 0214547
    • F. Lindemann, Über die Zahl $\pi$, Math. Ann. 20 (1882). K. Mahler, Zur Approximation der Exponential Funktion und des Logarithmus, J. Reine Angew. Math. 166 (1931/32). D. Mardohai-Boltouski, On some properties of transcendental numbers of the first class, Mat. Sb. 34 (1927).
  • Carlos J. Moreno, The values of exponential polynomials at algebraic points. II, Diophantine approximation and its applications (Proc. Conf., Washington, D.C., 1972) Academic Press, New York, 1973, pp. 111–128. MR 0347746
  • A. B. Šidlovskiĭ, On transcendentality of the values of a class of entire functions satisfying linear differential equations, Dokl. Akad. Nauk SSSR (N.S.) 105 (1955), 35–37 (Russian). MR 0076806
    • C. Siegel, Über einige Anwendungen Diophantischer Approximationen, Abh. Preuss. Akad. Wiss. 1929/30, No. 1.
  • Carl Ludwig Siegel, Transcendental Numbers, Annals of Mathematics Studies, No. 16, Princeton University Press, Princeton, N. J., 1949. MR 0032684
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 186 (1973), 17-31
  • MSC: Primary 10F35
  • DOI: https://doi.org/10.1090/S0002-9947-1973-0325545-2
  • MathSciNet review: 0325545