Duke Mathematical Journal

The proof of the central limit theorem for theta sums

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

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

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

First available in Project Euclid: 20 February 2004

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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

Export citation


  • [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.