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Mat. Zametki, 1996, Volume 60, Issue 5, Pages 681–691 (Mi mz1881)  

This article is cited in 7 scientific papers (total in 7 papers)

Algebraic independence of the periods of abelian integrals

K. G. Vasil'ev

M. V. Lomonosov Moscow State University

Abstract: Abelian integrals of the first and the second kind are proved to have two algebraically independent periods. Some corollaries concerning the algebraic independence of the values of Euler's beta and gamma functions at rational points are derived.

DOI: https://doi.org/10.4213/mzm1881

Full text: PDF file (218 kB)
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English version:
Mathematical Notes, 1996, 60:5, 510–518

Bibliographic databases:

UDC: 511.364
Received: 16.02.1995
Revised: 18.11.1995

Citation: K. G. Vasil'ev, “Algebraic independence of the periods of abelian integrals”, Mat. Zametki, 60:5 (1996), 681–691; Math. Notes, 60:5 (1996), 510–518

Citation in format AMSBIB
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\paper Algebraic independence of the periods of abelian integrals
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\vol 60
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\pages 681--691
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\vol 60
\issue 5
\pages 510--518
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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. Grinspan, P, “Measures of simultaneous approximation for quasi-periods of abelian varieties”, Journal of Number Theory, 94:1 (2002), 136  crossref  mathscinet  zmath  isi  scopus  scopus
    2. Waldschmidt, M, “Transcendence of periods: The state of the art”, Pure and Applied Mathematics Quarterly, 2:2 (2006), 435  crossref  mathscinet  zmath  isi
    3. Murty, MR, “Transcendental values of the digamma function”, Journal of Number Theory, 125:2 (2007), 298  crossref  mathscinet  zmath  isi  scopus  scopus
    4. Waldschmidt M., “Transcendance of Periods: State of Cognition”, Proceedings of the Tunisian Mathematical Society, Volume 11, eds. Trimeche K., Zarati S., Nova Science Publishers, Inc, 2007, 89–116  mathscinet  isi
    5. Gun, S, “Linear independence of digamma function and a variant of a conjecture of Rohrlich”, Journal of Number Theory, 129:8 (2009), 1858  crossref  mathscinet  zmath  isi  scopus
    6. Murty M.R., Murty V.K., “Transcendental Values of Class Group l-Functions”, Math. Ann., 351:4 (2011), 835–855  crossref  mathscinet  zmath  isi  scopus  scopus
    7. Menken H., Asan A., “On some transcendental values of the -adic gamma function”, Advances in Non-Archimedean Analysis, Contemporary Mathematics, 665, eds. Glockner H., Escassut A., Shamseddine K., Amer Mathematical Soc, 2016, 159–164  crossref  mathscinet  zmath  isi
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