Duke Mathematical Journal

The proof of the central limit theorem for theta sums

W. B. Jurkat and J. W. Van Horne

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Article information

Source
Duke Math. J., Volume 48, Number 4 (1981), 873-885.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1077314936

Digital Object Identifier
doi:10.1215/S0012-7094-81-04848-1

Mathematical Reviews number (MathSciNet)
MR782582

Zentralblatt MATH identifier
0491.10027

Subjects
Primary: 11L03: Trigonometric and exponential sums, general
Secondary: 60F05: Central limit and other weak theorems

Citation

Jurkat, W. B.; Van Horne, J. W. The proof of the central limit theorem for theta sums. Duke Math. J. 48 (1981), no. 4, 873--885. doi:10.1215/S0012-7094-81-04848-1. https://projecteuclid.org/euclid.dmj/1077314936


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References

  • [1] Tom M. Apostol, Introduction to analytic number theory, Springer-Verlag, New York, 1976.
  • [2] H. Fiedler, W. Jurkat, and O. Körner, Asymptotic expansions of finite theta series, Acta Arith. 32 (1977), no. 2, 129–146.
  • [3] G. H. Hardy and J. Littlewood, Some problems in diophantine approximation, Acta Math. 37 (1914), 193–238.
  • [4] W. B. Jurkat and J. W. Van Horne, On the central limit theorem for theta series, to appear in Mich. Math. J.
  • [5] M. Kac, Note on Power Series with Big Gaps, Amer. J. Math. 61 (1939), 473–476.
  • [6] M. Kac, On the distribution of values of sums of the type $\sum f(2\sp k t)$, Ann. of Math. (2) 47 (1946), 33–49.
  • [7] J. F. C. Kingman and S. J. Taylor, Introduction to measure and probability, Cambridge University Press, London, 1966.
  • [8] R. Salem and A. Zygmund, On lacunary trigonometric series, Proc. Nat. Acad. Sci. U. S. A. 33 (1947), 333–338.