Duverney, Daniel; Tachiya, Yohei Algebraic independence of certain infinite products involving the Fibonacci numbers. (English) Zbl 1477.11127 Proc. Japan Acad., Ser. A 97, No. 5, 29-31 (2021). Reviewer: Jaroslav Hančl (Ostrava) MSC: 11J85 11B39 11F27 PDF BibTeX XML Cite \textit{D. Duverney} and \textit{Y. Tachiya}, Proc. Japan Acad., Ser. A 97, No. 5, 29--31 (2021; Zbl 1477.11127) Full Text: DOI arXiv OpenURL
Duverney, D.; Suzuki, Y.; Tachiya, Y. Linear independence results for sums of reciprocals of Fibonacci and Lucas numbers. (English) Zbl 1474.11129 Acta Math. Hung. 162, No. 1, 375-392 (2020). MSC: 11J72 11A41 PDF BibTeX XML Cite \textit{D. Duverney} et al., Acta Math. Hung. 162, No. 1, 375--392 (2020; Zbl 1474.11129) Full Text: DOI arXiv OpenURL
Zudilin, Wadim On the irrationality of generalized \(q\)-logarithm. (English) Zbl 1415.11099 Res. Number Theory 2, Paper No. 15, 10 p. (2016). MSC: 11J72 11C20 33D15 41A20 PDF BibTeX XML Cite \textit{W. Zudilin}, Res. Number Theory 2, Paper No. 15, 10 p. (2016; Zbl 1415.11099) Full Text: DOI arXiv OpenURL
Bundschuh, P. Remarks on linear independence of \(q\)-harmonic series. (English. Russian original) Zbl 1345.11048 J. Math. Sci., New York 180, No. 5, 550-555 (2012); translation from Fundam. Prikl. Mat. 16, No. 5, 31-39 (2010). MSC: 11J72 11J91 PDF BibTeX XML Cite \textit{P. Bundschuh}, J. Math. Sci., New York 180, No. 5, 550--555 (2012; Zbl 1345.11048); translation from Fundam. Prikl. Mat. 16, No. 5, 31--39 (2010) Full Text: DOI OpenURL
Jouhet, Frédéric; Mosaki, Elie Diophantine properties for \(q\)-analogues of Dirichlet’s beta function at positive integers. (English) Zbl 1217.11069 Trans. Am. Math. Soc. 363, No. 3, 1533-1554 (2011). Reviewer: József Sándor (Cluj-Napoca) MSC: 11J72 11M41 33D15 PDF BibTeX XML Cite \textit{F. Jouhet} and \textit{E. Mosaki}, Trans. Am. Math. Soc. 363, No. 3, 1533--1554 (2011; Zbl 1217.11069) Full Text: DOI arXiv OpenURL
Van Assche, Walter Hermite-Padé rational approximation to irrational numbers. (English) Zbl 1239.11078 Comput. Methods Funct. Theory 10, No. 2, 585-602 (2010). Reviewer: Peter Bundschuh (Köln) MSC: 11J72 11J82 41A21 PDF BibTeX XML Cite \textit{W. Van Assche}, Comput. Methods Funct. Theory 10, No. 2, 585--602 (2010; Zbl 1239.11078) Full Text: DOI OpenURL
Coussement, J.; Smet, C. Irrationality proof of certain Lambert series using little \(q\)-Jacobi polynomials. (English) Zbl 1180.41011 J. Comput. Appl. Math. 233, No. 3, 680-690 (2009). Reviewer: Jacek Gilewicz (Marseille) MSC: 41A21 PDF BibTeX XML Cite \textit{J. Coussement} and \textit{C. Smet}, J. Comput. Appl. Math. 233, No. 3, 680--690 (2009; Zbl 1180.41011) Full Text: DOI arXiv OpenURL
Bézivin, Jean-Paul Irrationality of certain sums of series. (Irrationalité de certaines sommes de séries.) (French) Zbl 1202.11039 Manuscr. Math. 126, No. 1, 41-47 (2008). Reviewer: Michel Waldschmidt (Paris) MSC: 11J72 PDF BibTeX XML Cite \textit{J.-P. Bézivin}, Manuscr. Math. 126, No. 1, 41--47 (2008; Zbl 1202.11039) Full Text: DOI OpenURL
Matala-aho, Tapani On irrationality measures of \(\sum^{\infty}_{l=0}d^{l} / \prod^l_{j=1}(1+d^jr+d^{2j}s)\). (English) Zbl 1214.11084 J. Number Theory 128, No. 1, 1-16 (2008). Reviewer: Peter Bundschuh (Köln) MSC: 11J82 11J72 PDF BibTeX XML Cite \textit{T. Matala-aho}, J. Number Theory 128, No. 1, 1--16 (2008; Zbl 1214.11084) Full Text: DOI OpenURL
Matala-Aho, Tapani; Prévost, Marc Quantitative irrationality for sums of reciprocals of Fibonacci and Lucas numbers. (English) Zbl 1104.11040 Ramanujan J. 11, No. 2, 249-261 (2006). Reviewer: Jaroslav Hančl (Ostrava) MSC: 11J82 11B39 PDF BibTeX XML Cite \textit{T. Matala-Aho} and \textit{M. Prévost}, Ramanujan J. 11, No. 2, 249--261 (2006; Zbl 1104.11040) Full Text: DOI OpenURL
Matala-aho, Tapani; Väänänen, Keijo; Zudilin, Wadim New irrationality measures for \(q\)-logarithms. (English) Zbl 1158.11033 Math. Comput. 75, No. 254, 879-889 (2006). Reviewer: Peter Bundschuh (Köln) MSC: 11J82 33D15 PDF BibTeX XML Cite \textit{T. Matala-aho} et al., Math. Comput. 75, No. 254, 879--889 (2006; Zbl 1158.11033) Full Text: DOI OpenURL
Zudilin, W. Approximations to \(q\)-logarithms and \(q\)-dilogarithms, with applications to \(q\)-zeta values. (English) Zbl 1088.11052 J. Math. Sci., New York 137, No. 2, 4617-4633 (2006); translation from Zap. Nauchn. Semin. POMI 322, 107-124 (2005). Reviewer: Maurice Mignotte (Strasbourg) MSC: 11J82 11M41 33D15 PDF BibTeX XML Cite \textit{W. Zudilin}, J. Math. Sci., New York 137, No. 2, 107--124 (2005; Zbl 1088.11052); translation from Zap. Nauchn. Semin. POMI 322, 107--124 (2005) Full Text: DOI EuDML OpenURL
Matala-aho, Tapani; Prévost, Marc Irrationality measures for the series of reciprocals from recurrence sequences. (English) Zbl 1069.11030 J. Number Theory 96, No. 2, 275-292 (2002). Reviewer: Boris Adamczewski (Lyon) MSC: 11J82 PDF BibTeX XML Cite \textit{T. Matala-aho} and \textit{M. Prévost}, J. Number Theory 96, No. 2, 275--292 (2002; Zbl 1069.11030) Full Text: DOI Link OpenURL
Prévost, M. On the irrationality of \(\sum \frac{t^n} {A\alpha^n+ B\beta^n}\). (English) Zbl 0920.11044 J. Number Theory 73, No. 2, 139-161 (1998). Reviewer: P.Bundschuh (Köln) MSC: 11J72 11J82 41A21 PDF BibTeX XML Cite \textit{M. Prévost}, J. Number Theory 73, No. 2, 139--161 (1998; Zbl 0920.11044) Full Text: DOI OpenURL
Duverney, Daniel Concerning the series \(\sum_{n=1}^{+\infty} {x^ n\over q^ n-1}\). (A propos de la série \(\sum_{n=1}^{+\infty} {x^ n\over q^ n-1}\).) (French) Zbl 0867.11054 J. Théor. Nombres Bordx. 8, No. 1, 173-181 (1996). Reviewer: P.Bundschuh (Köln) MSC: 11J72 11J82 PDF BibTeX XML Cite \textit{D. Duverney}, J. Théor. Nombres Bordx. 8, No. 1, 173--181 (1996; Zbl 0867.11054) Full Text: DOI Numdam EuDML EMIS OpenURL