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Izv. RAN. Ser. Mat., 2011, Volume 75, Issue 1, Pages 181–224 (Mi izv4062)  

This article is cited in 1 scientific paper (total in 1 paper)

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

I. P. Rochev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

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.

DOI: https://doi.org/10.4213/im4062

Full text: PDF file (746 kB)
References (in Russian): PDF file   HTML файл

English version:
Izvestiya: Mathematics, 2011, 75:1, 177–221

Bibliographic databases:

UDC: 511
MSC: 11J72, 11J82
Received: 26.11.2008
Revised: 22.10.2009

Citation: I. P. Rochev, “On linear independence of values of certain $q$-series”, Izv. RAN. Ser. Mat., 75:1 (2011), 181–224; Izv. Math., 75:1 (2011), 177–221

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Vaananen K., “Irrationality Measures of Numbers Related To Some Q-Basic Hypergeometric Series”, Math. Scand., 114:2 (2014), 254–263  mathscinet  zmath  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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