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Uspekhi Mat. Nauk, 2008, Volume 63, Issue 6(384), Pages 31–38 (Mi umn9250)  

This article is cited in 4 scientific papers (total in 4 papers)

Limit theorem for trigonometric sums. Theory of curlicues

Ya. G. Sinaiab

a L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
b Princeton University

Abstract: This paper is a discussion of the behaviour of the trigonometric sums $\sum\exp\{2\pi\alpha n^2\}$ and their limiting distribution as a function of $N$. The analysis is based upon another application of the renormalization group theory.

DOI: https://doi.org/10.4213/rm9250

Full text: PDF file (597 kB)
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English version:
Russian Mathematical Surveys, 2008, 63:6, 1023–1029

Bibliographic databases:

UDC: 517.987.5
MSC: Primary 37A45; Secondary 11A55 60Fxx
Received: 15.08.2008

Citation: Ya. G. Sinai, “Limit theorem for trigonometric sums. Theory of curlicues”, Uspekhi Mat. Nauk, 63:6(384) (2008), 31–38; Russian Math. Surveys, 63:6 (2008), 1023–1029

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Alonso-Sanz R., “Curlicues with memory”, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 20:7 (2010), 2225–2240  crossref  mathscinet  zmath  isi  elib  scopus
    2. Cellarosi F., “Limiting curlicue measures for theta sums”, Ann. Inst. Henri Poincaré Probab. Stat., 47:2 (2011), 466–497  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. Boca F.P., Vandehey J., “On Certain Statistical Properties of Continued Fractions with Even and with Odd Partial Quotients”, Acta Arith., 156:3 (2012), 201–221  crossref  mathscinet  zmath  isi  elib  scopus
    4. Tanguy Rivoal, Stéphane Seuret, “Hardy-Littlewood series and even continued fractions”, JAMA, 125:1 (2015), 175  crossref  mathscinet  zmath  isi  scopus
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