The proof of the central limit theorem for theta sums
W. B. Jurkat and J. W. Van Horne
Source: Duke Math. J. Volume 48, Number 4
(1981), 873-885.
First Page:
Show
Hide
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
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077314936
Mathematical Reviews number (MathSciNet): MR782582
Zentralblatt MATH identifier: 0491.10027
Digital Object Identifier: doi:10.1215/S0012-7094-81-04848-1
References
[1] Tom M. Apostol, Introduction to analytic number theory, Springer-Verlag, New York, 1976.
Mathematical Reviews (MathSciNet): MR55:7892
Zentralblatt MATH: 0335.10001
[2] H. Fiedler, W. Jurkat, and O. Körner, Asymptotic expansions of finite theta series, Acta Arith. 32 (1977), no. 2, 129–146.
Mathematical Reviews (MathSciNet): MR58:27832
Zentralblatt MATH: 0308.10021
[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.
Mathematical Reviews (MathSciNet): MR646372
Digital Object Identifier: doi:10.1307/mmj/1029002615
Project Euclid: euclid.mmj/1029002615
[5] M. Kac, Note on Power Series with Big Gaps, Amer. J. Math. 61 (1939), 473–476.
Zentralblatt MATH: 0020.37603
Mathematical Reviews (MathSciNet): MR1507389
Digital Object Identifier: doi:10.2307/2371514
JSTOR: links.jstor.org
[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.
Mathematical Reviews (MathSciNet): MR7,436f
Zentralblatt MATH: 0063.03091
Digital Object Identifier: doi:10.2307/1969033
JSTOR: links.jstor.org
[7] J. F. C. Kingman and S. J. Taylor, Introduction to measure and probability, Cambridge University Press, London, 1966.
Mathematical Reviews (MathSciNet): MR36:1601
Zentralblatt MATH: 0171.38603
[8] R. Salem and A. Zygmund, On lacunary trigonometric series, Proc. Nat. Acad. Sci. U. S. A. 33 (1947), 333–338.
Mathematical Reviews (MathSciNet): MR9,181d
Zentralblatt MATH: 0029.11902
Digital Object Identifier: doi:10.1073/pnas.33.11.333
JSTOR: links.jstor.org
Duke Mathematical Journal