Faverjon, Colin; Poulet, Marina An algorithm to recognize regular singular Mahler systems. (English) Zbl 07582818 Math. Comput. 91, No. 338, 2905-2928 (2022). MSC: 65Q10 39A06 68W30 11B85 PDF BibTeX XML Cite \textit{C. Faverjon} and \textit{M. Poulet}, Math. Comput. 91, No. 338, 2905--2928 (2022; Zbl 07582818) Full Text: DOI arXiv OpenURL
Fernandes, Gwladys A survey on the hypertranscendence of the solutions of the Schröder’s, Böttcher’s and Abel’s equations. (English) Zbl 07615261 Bostan, Alin (ed.) et al., Transcendence in algebra, combinatorics, geometry and number theory. TRANS19 – transient transcendence in Transylvania, Brașov, Romania, May 13–17, 2019. Revised and extended contributions. Cham: Springer. Springer Proc. Math. Stat. 373, 91-125 (2021). MSC: 30D05 30D15 37F10 PDF BibTeX XML Cite \textit{G. Fernandes}, Springer Proc. Math. Stat. 373, 91--125 (2021; Zbl 07615261) Full Text: DOI arXiv OpenURL
Adamczewski, Boris; Dreyfus, Thomas; Hardouin, Charlotte Hypertranscendence and linear difference equations. (English) Zbl 1479.39004 J. Am. Math. Soc. 34, No. 2, 475-503 (2021). MSC: 39A13 39A70 39A06 12H05 12H10 34M15 39A12 PDF BibTeX XML Cite \textit{B. Adamczewski} et al., J. Am. Math. Soc. 34, No. 2, 475--503 (2021; Zbl 1479.39004) Full Text: DOI arXiv OpenURL
Coons, Michael Degree-one Mahler functions: asymptotics, applications and speculations. (English) Zbl 1461.11109 Bull. Aust. Math. Soc. 102, No. 3, 399-409 (2020). Reviewer: Tanguy Rivoal (Grenoble) MSC: 11J91 11B85 30B10 68R15 PDF BibTeX XML Cite \textit{M. Coons}, Bull. Aust. Math. Soc. 102, No. 3, 399--409 (2020; Zbl 1461.11109) Full Text: DOI OpenURL
Pellarin, Federico An introduction to Mahler’s method for transcendence and algebraic independence. (English) Zbl 1440.11137 Böckle, Gebhard (ed.) et al., \(t\)-motives: Hodge structures, transcendence and other motivic aspects. EMS Series of Congress Reports. Zürich: European Mathematical Society (EMS). 297-349 (2020). MSC: 11J91 11J81 PDF BibTeX XML Cite \textit{F. Pellarin}, in: \(t\)-motives: Hodge structures, transcendence and other motivic aspects. Zürich: European Mathematical Society (EMS). 297--349 (2020; Zbl 1440.11137) Full Text: DOI arXiv OpenURL
Adamczewski, Boris Mahler’s method. (English) Zbl 1451.11002 Doc. Math. Extra Vol., Mahler Selecta, 95-122 (2019). MSC: 11-03 11-02 11J81 11J82 11J85 PDF BibTeX XML Cite \textit{B. Adamczewski}, Doc. Math. Extra Vol., 95--122 (2019; Zbl 1451.11002) Full Text: DOI OpenURL
Coons, Michael; Spiegelhofer, Lukas Number theoretic aspects of regular sequences. (English) Zbl 1423.11063 Berthé, Valérie (ed.) et al., Sequences, groups, and number theory. Cham: Birkhäuser. Trends Math., 37-87 (2018). MSC: 11B83 11B85 11-02 PDF BibTeX XML Cite \textit{M. Coons} and \textit{L. Spiegelhofer}, in: Sequences, groups, and number theory. Cham: Birkhäuser. 37--87 (2018; Zbl 1423.11063) Full Text: DOI OpenURL
Roques, Julien On the algebraic relations between Mahler functions. (English) Zbl 1376.39002 Trans. Am. Math. Soc. 370, No. 1, 321-355 (2018). MSC: 39A06 12H10 PDF BibTeX XML Cite \textit{J. Roques}, Trans. Am. Math. Soc. 370, No. 1, 321--355 (2018; Zbl 1376.39002) Full Text: DOI Link OpenURL
Bugeaud, Yann; Yao, Jia-Yan Hankel determinants, Padé approximations, and irrationality exponents for \(p\)-adic numbers. (English) Zbl 1435.11094 Ann. Mat. Pura Appl. (4) 196, No. 3, 929-946 (2017). MSC: 11J72 11J82 05A10 05A15 11B50 11B85 PDF BibTeX XML Cite \textit{Y. Bugeaud} and \textit{J.-Y. Yao}, Ann. Mat. Pura Appl. (4) 196, No. 3, 929--946 (2017; Zbl 1435.11094) Full Text: DOI OpenURL
Kisielewski, Tomasz Criteria for regularity of Mahler power series and Becker’s conjecture. (English) Zbl 1384.11049 J. Number Theory 174, 456-486 (2017). Reviewer: Peter Jau-shyong Shiue (Las Vegas) MSC: 11B85 11J81 PDF BibTeX XML Cite \textit{T. Kisielewski}, J. Number Theory 174, 456--486 (2017; Zbl 1384.11049) Full Text: DOI arXiv OpenURL
Bell, Jason P.; Coons, Michael Transcendence tests for Mahler functions. (English) Zbl 1365.11092 Proc. Am. Math. Soc. 145, No. 3, 1061-1070 (2017). Reviewer: Robert F. Tichy (Graz) MSC: 11J91 39A06 PDF BibTeX XML Cite \textit{J. P. Bell} and \textit{M. Coons}, Proc. Am. Math. Soc. 145, No. 3, 1061--1070 (2017; Zbl 1365.11092) Full Text: DOI arXiv OpenURL
Bundschuh, Peter; Väänänen, Keijo Guided by Schwarz’ functions: a walk through the garden of Mahler’s transcendence method. (English) Zbl 1407.11090 Sander, Jürgen (ed.) et al., From arithmetic to zeta-functions. Number theory in memory of Wolfgang Schwarz. Cham: Springer. 91-101 (2016). MSC: 11J91 11J81 PDF BibTeX XML Cite \textit{P. Bundschuh} and \textit{K. Väänänen}, in: From arithmetic to zeta-functions. Number theory in memory of Wolfgang Schwarz. Cham: Springer. 91--101 (2016; Zbl 1407.11090) Full Text: DOI OpenURL
Bell, Jason P.; Bugeaud, Yann; Coons, Michael Diophantine approximation of Mahler numbers. (English) Zbl 1320.11064 Proc. Lond. Math. Soc. (3) 110, No. 5, 1157-1206 (2015). Reviewer: Jan Šustek (Ostrava) MSC: 11J82 11B85 41A21 PDF BibTeX XML Cite \textit{J. P. Bell} et al., Proc. Lond. Math. Soc. (3) 110, No. 5, 1157--1206 (2015; Zbl 1320.11064) Full Text: DOI arXiv OpenURL
Coons, Michael On the rational approximation of the sum of the reciprocals of the Fermat numbers. (English) Zbl 1271.11075 Ramanujan J. 30, No. 1, 39-65 (2013); addendum ibid. 37, No. 1, 109–111 (2015). Reviewer: Jaroslav Hančl (Ostrava) MSC: 11J82 41A21 PDF BibTeX XML Cite \textit{M. Coons}, Ramanujan J. 30, No. 1, 39--65 (2013; Zbl 1271.11075) Full Text: DOI arXiv OpenURL
Bundschuh, Peter Transcendence and algebraic independence of series related to Stern’s sequence. (English) Zbl 1288.11070 Int. J. Number Theory 8, No. 2, 361-376 (2012). MSC: 11J81 11B83 11J25 11J91 11J87 PDF BibTeX XML Cite \textit{P. Bundschuh}, Int. J. Number Theory 8, No. 2, 361--376 (2012; Zbl 1288.11070) Full Text: DOI OpenURL
Wang, Tianqin \(p\)-adic transcendence and \(p\)-adic transcendence measures for the values of Mahler type functions. (English) Zbl 1110.11022 Acta Math. Sin., Engl. Ser. 22, No. 1, 187-194 (2006). Reviewer: Peter Bundschuh (Köln) MSC: 11J91 11J81 11J82 11J85 PDF BibTeX XML Cite \textit{T. Wang}, Acta Math. Sin., Engl. Ser. 22, No. 1, 187--194 (2006; Zbl 1110.11022) Full Text: DOI OpenURL
Töpfer, Th. Simultaneous approximation measures for functions satisfying generalized functional equations of Mahler type. (English) Zbl 0873.11044 Abh. Math. Semin. Univ. Hamb. 66, 177-201 (1996). Reviewer: J.H.Loxton (North Ryde) MSC: 11J82 11J13 11J91 PDF BibTeX XML Cite \textit{Th. Töpfer}, Abh. Math. Semin. Univ. Hamb. 66, 177--201 (1996; Zbl 0873.11044) Full Text: DOI OpenURL
Töpfer, Thomas An axiomatization of Nesterenko’s method and applications on Mahler functions. II. (English) Zbl 0839.11028 Compos. Math. 95, No. 3, 323-342 (1995). Reviewer: M.Waldschmidt (Paris) MSC: 11J85 11J91 30D05 39B62 PDF BibTeX XML Cite \textit{T. Töpfer}, Compos. Math. 95, No. 3, 323--342 (1995; Zbl 0839.11028) Full Text: Numdam EuDML OpenURL
Becker, Paul-Georg; Töpfer, Thomas Transcendency results for sums of reciprocals of linear recurrences. (English) Zbl 0835.11026 Math. Nachr. 168, 5-17 (1994). Reviewer: J.Hančl (Ostrava) MSC: 11J81 11B37 PDF BibTeX XML Cite \textit{P.-G. Becker} and \textit{T. Töpfer}, Math. Nachr. 168, 5--17 (1994; Zbl 0835.11026) Full Text: DOI OpenURL
Nishioka, Kumiko Algebraic independence by Mahler’s method and \(S\)-unit equations. (English) Zbl 0802.11029 Compos. Math. 92, No. 1, 87-110 (1994). Reviewer: P.-G.Becker (Köln) MSC: 11J86 11D99 PDF BibTeX XML Cite \textit{K. Nishioka}, Compos. Math. 92, No. 1, 87--110 (1994; Zbl 0802.11029) Full Text: Numdam EuDML OpenURL
Becker, Paul-Georg; Bergweiler, Walter Transcendency of local conjugacies in complex dynamics and transcendency of their values. (English) Zbl 0808.11045 Manuscr. Math. 81, No. 3-4, 329-337 (1993). Reviewer: F.Gramain (Saint-Etienne) MSC: 11J91 30D05 37B99 PDF BibTeX XML Cite \textit{P.-G. Becker} and \textit{W. Bergweiler}, Manuscr. Math. 81, No. 3--4, 329--337 (1993; Zbl 0808.11045) Full Text: DOI EuDML OpenURL
Bézivin, Jean-Paul Solutions rationnelles de certaines équations fonctionnelles. (Rational solutions of certain functional equations). (French) Zbl 0661.10018 Aequationes Math. 36, No. 1, 112-124 (1988). Reviewer: A.J.van der Poorten MSC: 11B37 39B05 13J05 PDF BibTeX XML Cite \textit{J.-P. Bézivin}, Aequationes Math. 36, No. 1, 112--124 (1988; Zbl 0661.10018) Full Text: DOI EuDML OpenURL
Nishioka, Keiji Algebraic function solutions of a certain class of functional equations. (English) Zbl 0568.12014 Arch. Math. 44, 330-335 (1985). Reviewer: John H. Loxton MSC: 11J81 11J91 12H05 39B99 PDF BibTeX XML Cite \textit{K. Nishioka}, Arch. Math. 44, 330--335 (1985; Zbl 0568.12014) Full Text: DOI OpenURL
Mahler, K. Fifty years as a Mathematician. (English) Zbl 0482.10002 J. Number Theory 14, 121-155 (1982). MSC: 11-03 01A70 11Hxx 11Jxx PDF BibTeX XML Cite \textit{K. Mahler}, J. Number Theory 14, 121--155 (1982; Zbl 0482.10002) Full Text: DOI OpenURL
Masser, D. W. A vanishing theorem for power series. (English) Zbl 0481.10034 Invent. Math. 67, 275-296 (1982). MSC: 11J81 30B10 32A05 PDF BibTeX XML Cite \textit{D. W. Masser}, Invent. Math. 67, 275--296 (1982; Zbl 0481.10034) Full Text: DOI EuDML OpenURL
Galochkin, A. I. Transcendence measure of values of functions satisfying certain functional equations. (English) Zbl 0444.10029 Math. Notes 27, 83-88 (1980). MSC: 11J81 PDF BibTeX XML Cite \textit{A. I. Galochkin}, Math. Notes 27, 83--88 (1980; Zbl 0444.10029) Full Text: DOI OpenURL
Kubota, K. K. On the algebraic independence of holomorphic solutions of certain functional equations and their values. (English) Zbl 0359.10030 Math. Ann. 227, 9-50 (1977). MSC: 11J81 PDF BibTeX XML Cite \textit{K. K. Kubota}, Math. Ann. 227, 9--50 (1977; Zbl 0359.10030) Full Text: DOI EuDML OpenURL
Loxton, J. H.; van der Poorten, A. J. On the growth of recurrence sequences. (English) Zbl 0348.10007 Math. Proc. Camb. Philos. Soc. 81, 369-376 (1977). MSC: 11B37 PDF BibTeX XML Cite \textit{J. H. Loxton} and \textit{A. J. van der Poorten}, Math. Proc. Camb. Philos. Soc. 81, 369--376 (1977; Zbl 0348.10007) Full Text: DOI OpenURL
Loxton, J. H.; van der Poorten, A. J. Arithmetic properties of certain functions in several variables. III. (English) Zbl 0339.10028 Bull. Aust. Math. Soc. 16, 15-47 (1977). MSC: 11J81 39B99 PDF BibTeX XML Cite \textit{J. H. Loxton} and \textit{A. J. van der Poorten}, Bull. Aust. Math. Soc. 16, 15--47 (1977; Zbl 0339.10028) Full Text: DOI OpenURL
Loxton, J. H.; van der Poorten, A. J. Arithmetic properties of certain functions in several variables. (English) Zbl 0339.10026 J. Number Theory 9, 87-106 (1977). MSC: 11J81 39B99 PDF BibTeX XML Cite \textit{J. H. Loxton} and \textit{A. J. van der Poorten}, J. Number Theory 9, 87--106 (1977; Zbl 0339.10026) Full Text: DOI OpenURL
Loxton, J. H.; van der Poorten, A. J. On algebraic functions satisfying a class of functional equations. (English) Zbl 0339.12002 Aequationes Math. 14, 413-420 (1976). MSC: 11R04 39B99 30D30 PDF BibTeX XML Cite \textit{J. H. Loxton} and \textit{A. J. van der Poorten}, Aequationes Math. 14, 413--420 (1976; Zbl 0339.12002) Full Text: DOI EuDML OpenURL
Mahler, Kurt On the transcendency of the solutions of a special class of functional equations. (English) Zbl 0316.10021 Bull. Aust. Math. Soc. 13, 389-410 (1975). MSC: 11J81 39B99 PDF BibTeX XML Cite \textit{K. Mahler}, Bull. Aust. Math. Soc. 13, 389--410 (1975; Zbl 0316.10021) Full Text: DOI OpenURL
Osgood, Charles F. The simultaneous diophantine approximation of values of functions satisfying certain n variable q-difference equations. (English) Zbl 0288.10011 J. Number Theory 6, 374-400 (1974). MSC: 11J17 35R10 PDF BibTeX XML Cite \textit{C. F. Osgood}, J. Number Theory 6, 374--400 (1974; Zbl 0288.10011) Full Text: DOI OpenURL