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Izvestiya: Mathematics, 2011, Volume 75, Issue 1, Pages 177–221
DOI: https://doi.org/10.1070/IM2011v075n01ABEH002531 (Mi im4062) 		 
This article is cited in 4 scientific papers (total in 4 papers)

On linear independence of values of certain $q$-series

I. P. Rochev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (520 kB) Citations (4) Russian version article
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DOI: https://doi.org/10.1070/IM2011v075n01ABEH002531
Abstract: We obtain qualitative and quantitative results on the linear independence of the values of functions in a fairly wide class generalizing $q$-hypergeometric series and of their derivatives at algebraic points. The results are proved in both the Archimedean and $p$-adic cases.
Keywords: algebraic number field, absolute height of an algebraic number, $q$-series, $q$-exponential function, $q$-logarithm, linear independence, linear independence measure, Hankel determinant, cyclotomic polynomial.
Received: 26.11.2008
Revised: 22.10.2009
Bibliographic databases:
Document Type: Article
UDC: 511
MSC: 11J72, 11J82
Language: English
Original paper language: Russian
Citation: I. P. Rochev, “On linear independence of values of certain $q$-series”, Izv. Math., 75:1 (2011), 177–221
Citation in format AMSBIB
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\by I.~P.~Rochev
\paper On linear independence of values of certain $q$-series
\jour Izv. Math.
\yr 2011
\vol 75
\issue 1
\pages 177--221
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Linking options:
  • https://www.mathnet.ru/eng/im4062
  • https://doi.org/10.1070/IM2011v075n01ABEH002531
  • https://www.mathnet.ru/eng/im/v75/i1/p181
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:598
    Russian version PDF:237
    English version PDF:12
    References:79
    First page:22
     
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