Duke Mathematical Journal

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.
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Primary Subjects: 11L03
Secondary Subjects: 60F05
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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
[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
[7] J. F. C. Kingman and S. J. Taylor, Introduction to measure and probability, Cambridge University Press, London, 1966.
Mathematical Reviews (MathSciNet): MR36:1601
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[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

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