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Mat. Zametki, 2005, Volume 78, Issue 4, Pages 608–613 (Mi mz2619)  

This article is cited in 9 scientific papers (total in 9 papers)

Linear and Algebraic Independence of $q$-Zeta Values

Yu. A. Pupyrev

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

Abstract: In the paper, results on linear and algebraic independence of $q$-series of the form $\zeta_q(s)=\sum_{n=1}^\infty\sigma_{s-1}(n)q^n$ over the field $\mathbb C(q)$ are obtained, where $\sigma_{s-1}(n)=\sum_{d\mid n}d^{s-1}$, $s=1,2,…$.

Funding Agency Grant Number
Russian Foundation for Basic Research 03-01-00359


DOI: https://doi.org/10.4213/mzm2619

Full text: PDF file (178 kB)
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English version:
Mathematical Notes, 2005, 78:4, 563–568

Bibliographic databases:

Document Type: Article
UDC: 511.3+517.51
Received: 04.04.2005

Citation: Yu. A. Pupyrev, “Linear and Algebraic Independence of $q$-Zeta Values”, Mat. Zametki, 78:4 (2005), 608–613; Math. Notes, 78:4 (2005), 563–568

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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. Bundschuh P., Zudilin W., “Irrationality measures for certain $q$-mathematical constants”, Math. Scand., 101:1 (2007), 104–122  mathscinet  zmath  isi  elib
    2. J.-P. Bézivin, “Indépendance linéaire et algébrique de fonctions liées à la fonction $q$-dzeta”, Ann. Fac. Sci. Toulouse Math. (6), 17:1 (2008), 23–36  crossref  mathscinet  zmath
    3. W. Zudilin, “Arithmetic hypergeometric series”, Russian Math. Surveys, 66:2 (2011), 369–420  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. Igarashi M., “Cyclic sum of certain parametrized multiple series”, J Number Theory, 131:3 (2011), 508–518  crossref  mathscinet  zmath  isi  elib
    5. Ohno Ya., Okuda J.-i., Zudilin W., “Cyclic Q-Mzsv Sum”, J. Number Theory, 132:1 (2012), 144–155  crossref  mathscinet  zmath  isi  elib
    6. Zudilin W., “on Three Theorems of Folsom, Ono and Rhoades”, Proc. Amer. Math. Soc., 143:4 (2015), PII S0002-9939(2014)12364-1, 1471–1476  crossref  mathscinet  zmath  isi
    7. Zudilin W., “Multiple Q-Zeta Brackets”, 3, no. 1, 2015, 119–130  crossref  zmath  isi
    8. Bachmann H., Kuehn U., “The algebra of generating functions for multiple divisor sums and applications to multiple zeta values”, Ramanujan J., 40:3 (2016), 605–648  crossref  mathscinet  zmath  isi  scopus
    9. Yuan H., Zhao J., “Bachmann?K?hn?s brackets and multiple zeta values at level N”, Manuscr. Math., 150:1-2 (2016), 177–210  crossref  mathscinet  zmath  isi  scopus
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