Bundschuh, Peter; Väänänen, Keijo Arithmetical results on some infinite products. (English) Zbl 1479.11128 Funct. Approximatio, Comment. Math. 63, No. 2, 181-188 (2020). Reviewer: Jaroslav Hančl (Ostrava) MSC: 11J81 11J82 11J91 PDF BibTeX XML Cite \textit{P. Bundschuh} and \textit{K. Väänänen}, Funct. Approximatio, Comment. Math. 63, No. 2, 181--188 (2020; Zbl 1479.11128) Full Text: DOI OpenURL
Tanuma, Yusuke Algebraic independence of the values of certain series and their derivatives involving the Hecke-Mahler series. (English) Zbl 1447.11083 J. Number Theory 210, 231-248 (2020). Reviewer: John H. Loxton (Greenwich) MSC: 11J85 11J91 PDF BibTeX XML Cite \textit{Y. Tanuma}, J. Number Theory 210, 231--248 (2020; Zbl 1447.11083) Full Text: DOI OpenURL
Mahler, Kurt Reprint: Remarks on a paper by W. Schwarz (1969). (English) Zbl 1457.11004 Doc. Math. Extra Vol., Mahler Selecta, 649-659 (2019). MSC: 11-03 11J85 PDF BibTeX XML Cite \textit{K. Mahler}, Doc. Math. Extra Vol., 649--659 (2019; Zbl 1457.11004) Full Text: DOI OpenURL
Mahler, Kurt Reprint: Arithmetic properties of a class of transcendental-transcendent functions (1930). (Reprint: Arithmetische Eigenschaften einer Klasse transzendental-transzendenter Funktionen (1930).) (German) Zbl 1465.11007 Doc. Math. Extra Vol., Mahler Selecta, 233-274 (2019). MSC: 11-03 11J81 11J91 PDF BibTeX XML Cite \textit{K. Mahler}, Doc. Math. Extra Vol., 233--274 (2019; Zbl 1465.11007) OpenURL
Mahler, Kurt Reprint: On the vanishing of power series of several variables in special point sequences (1930). (Reprint: Über das Verschwinden von Potenzreihen mehrerer Veränderlichen in speziellen Punktfolgen (1930).) (German) Zbl 1465.11006 Doc. Math. Extra Vol., Mahler Selecta, 217-232 (2019). MSC: 11-03 11J81 PDF BibTeX XML Cite \textit{K. Mahler}, Doc. Math. Extra Vol., 217--232 (2019; Zbl 1465.11006) Full Text: DOI OpenURL
Mahler, Kurt Reprint: Arithmetic properties of solutions of a class of functional equations (1929). (Reprint: Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen (1929).) (German. English summary) Zbl 1465.11005 Doc. Math. Extra Vol., Mahler Selecta, 191-216 (2019). MSC: 11-03 11J81 PDF BibTeX XML Cite \textit{K. Mahler}, Doc. Math. Extra Vol., 191--216 (2019; Zbl 1465.11005) OpenURL
Fernandes, Gwladys Regular extensions and algebraic relations between values of Mahler functions in positive characteristic. (English) Zbl 1445.11064 Trans. Am. Math. Soc. 372, No. 10, 7111-7140 (2019). Reviewer: Jaroslav Hančl (Ostrava) MSC: 11J81 11J72 11J85 PDF BibTeX XML Cite \textit{G. Fernandes}, Trans. Am. Math. Soc. 372, No. 10, 7111--7140 (2019; Zbl 1445.11064) Full Text: DOI arXiv OpenURL
Duverney, Daniel; Kurosawa, Takeshi; Shiokawa, Iekata Transcendence of numbers related with Cahen’s constant. (English) Zbl 1448.11139 Mosc. J. Comb. Number Theory 8, No. 1, 57-69 (2019). Reviewer: Mahadi Ddamulira (Saarbrücken) MSC: 11J81 PDF BibTeX XML Cite \textit{D. Duverney} et al., Mosc. J. Comb. Number Theory 8, No. 1, 57--69 (2019; Zbl 1448.11139) Full Text: DOI Euclid Link OpenURL
Adamczewski, Boris; Faverjon, Colin Mahler’s method, transcendence and linear relations: effective aspects. (Méthode de Mahler, transcendance et relations linéaires: aspects effectifs.) (French. English summary) Zbl 1441.11179 J. Théor. Nombres Bordx. 30, No. 2, 557-573 (2018). MSC: 11J81 11J72 PDF BibTeX XML Cite \textit{B. Adamczewski} and \textit{C. Faverjon}, J. Théor. Nombres Bordx. 30, No. 2, 557--573 (2018; Zbl 1441.11179) Full Text: DOI OpenURL
Bundschuh, Peter; Väänänen, Keijo Note on the Stern-Brocot sequence, some relatives, and their generating power series. (English. French summary) Zbl 1428.11132 J. Théor. Nombres Bordx. 30, No. 1, 195-202 (2018). Reviewer: Michel Waldschmidt (Paris) MSC: 11J81 11J91 11B37 PDF BibTeX XML Cite \textit{P. Bundschuh} and \textit{K. Väänänen}, J. Théor. Nombres Bordx. 30, No. 1, 195--202 (2018; Zbl 1428.11132) Full Text: DOI OpenURL
Fernandes, Gwladys Mahler’s method in positive characteristic: an analog of Ku. Nishioka’s theorem. (Méthode de Mahler en caractéristique non nulle: un analogue du théorème de Ku. Nishioka.) (French. English summary) Zbl 1436.11087 Ann. Inst. Fourier 68, No. 6, 2553-2580 (2018). Reviewer: Michel Waldschmidt (Paris) MSC: 11J85 PDF BibTeX XML Cite \textit{G. Fernandes}, Ann. Inst. Fourier 68, No. 6, 2553--2580 (2018; Zbl 1436.11087) Full Text: DOI arXiv OpenURL
Bundschuh, Peter; Väänänen, Keijo An application of Mahler’s method to continued fractions. (English) Zbl 1413.11087 Ann. Univ. Sci. Budap. Rolando Eötvös, Sect. Comput. 47, 167-172 (2018). Reviewer: Jaroslav Hančl (Ostrava) MSC: 11J81 11J70 PDF BibTeX XML Cite \textit{P. Bundschuh} and \textit{K. Väänänen}, Ann. Univ. Sci. Budap. Rolando Eötvös, Sect. Comput. 47, 167--172 (2018; Zbl 1413.11087) OpenURL
Tanaka, Taka-aki; Tanuma, Yusuke Algebraic independence of the values of the Hecke-Mahler series and its derivatives at algebraic numbers. (English) Zbl 1445.11068 Int. J. Number Theory 14, No. 9, 2369-2384 (2018). MSC: 11J85 11J91 PDF BibTeX XML Cite \textit{T.-a. Tanaka} and \textit{Y. Tanuma}, Int. J. Number Theory 14, No. 9, 2369--2384 (2018; Zbl 1445.11068) Full Text: DOI OpenURL
Amou, Masaaki; Väänänen, Keijo On algebraic independence of a class of infinite products. (English) Zbl 1419.11098 J. Number Theory 172, 114-132 (2017). MSC: 11J85 11J91 PDF BibTeX XML Cite \textit{M. Amou} and \textit{K. Väänänen}, J. Number Theory 172, 114--132 (2017; Zbl 1419.11098) Full Text: DOI Link 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
Bundschuh, Peter; Väänänen, Keijo Arithmetic properties of infinite products of cyclotomic polynomials. (English) Zbl 1341.11042 Bull. Aust. Math. Soc. 93, No. 3, 375-387 (2016). Reviewer: Jürgen Wolfart (Frankfurt am Main) MSC: 11J91 11J81 12H05 11J25 11J87 PDF BibTeX XML Cite \textit{P. Bundschuh} and \textit{K. Väänänen}, Bull. Aust. Math. Soc. 93, No. 3, 375--387 (2016; Zbl 1341.11042) Full Text: DOI OpenURL
Brent, Richard P.; Coons, Michael; Zudilin, Wadim Algebraic independence of Mahler functions via radial asymptotics. (English) Zbl 1415.11104 Int. Math. Res. Not. 2016, No. 2, 571-603 (2016). MSC: 11J85 PDF BibTeX XML Cite \textit{R. P. Brent} et al., Int. Math. Res. Not. 2016, No. 2, 571--603 (2016; Zbl 1415.11104) Full Text: DOI arXiv OpenURL
Bundschuh, Peter; Väänänen, Keijo Algebraic independence results on the generating Lambert series of the powers of a fixed integer. (English) Zbl 1378.11078 Hardy-Ramanujan J. 38, 36-44 (2016). Reviewer: Michel Waldschmidt (Paris) MSC: 11J91 11J81 39B32 PDF BibTeX XML Cite \textit{P. Bundschuh} and \textit{K. Väänänen}, Hardy-Ramanujan J. 38, 36--44 (2016; Zbl 1378.11078) Full Text: Link OpenURL
Bundschuh, Peter; Väänänen, Keijo Algebraic independence of reciprocal sums of powers of certain Fibonacci-type numbers. (English) Zbl 1395.11110 Funct. Approximatio, Comment. Math. 53, No. 1, 47-68 (2015). Reviewer: Takao Komatsu (Wuhan) MSC: 11J91 11J81 39B32 PDF BibTeX XML Cite \textit{P. Bundschuh} and \textit{K. Väänänen}, Funct. Approximatio, Comment. Math. 53, No. 1, 47--68 (2015; Zbl 1395.11110) Full Text: DOI Euclid OpenURL
Philippon, Patrice Galois groups and automatic numbers. (Groupes de Galois et nombres automatiques.) (French. English summary) Zbl 1391.11087 J. Lond. Math. Soc., II. Ser. 92, No. 3, 596-614 (2015). MSC: 11J81 12H10 37A45 26A18 PDF BibTeX XML Cite \textit{P. Philippon}, J. Lond. Math. Soc., II. Ser. 92, No. 3, 596--614 (2015; Zbl 1391.11087) Full Text: DOI arXiv OpenURL
Bundschuh, Peter; Väänänen, Keijo Algebraic independence of the generating functions of the stern polynomials and their twisted analogues. (English) Zbl 1323.11053 Arch. Math. 105, No. 2, 139-148 (2015). Reviewer: Jaroslav Hančl (Ostrava) MSC: 11J81 11J91 11B83 39B32 PDF BibTeX XML Cite \textit{P. Bundschuh} and \textit{K. Väänänen}, Arch. Math. 105, No. 2, 139--148 (2015; Zbl 1323.11053) Full Text: DOI OpenURL
Bundschuh, Peter; Väänänen, Keijo Algebraic independence of certain Mahler functions and of their values. (English) Zbl 1356.11044 J. Aust. Math. Soc. 98, No. 3, 289-310 (2015). Reviewer: Jürgen Wolfart (Frankfurt am Main) MSC: 11J91 11J81 11B39 11J85 39B32 PDF BibTeX XML Cite \textit{P. Bundschuh} and \textit{K. Väänänen}, J. Aust. Math. Soc. 98, No. 3, 289--310 (2015; Zbl 1356.11044) Full Text: DOI OpenURL
Kaneko, Hajime; Kurosawa, Takeshi; Tachiya, Yohei; Tanaka, Taka-Aki Explicit algebraic dependence formulae for infinite products related with Fibonacci and Lucas numbers. (English) Zbl 1331.11057 Acta Arith. 168, No. 2, 161-186 (2015). Reviewer: Michael Coons (Callaghan) MSC: 11J85 11J81 11J91 11B39 PDF BibTeX XML Cite \textit{H. Kaneko} et al., Acta Arith. 168, No. 2, 161--186 (2015; Zbl 1331.11057) Full Text: DOI OpenURL
Tanaka, Taka-Aki Arithmetic properties of solutions of certain functional equations with transformations represented by matrices including a negative entry. (English) Zbl 1303.11083 Tokyo J. Math. 37, No. 1, 211-223 (2014). Reviewer: Jaroslav Hančl (Ostrava) MSC: 11J85 11B39 PDF BibTeX XML Cite \textit{T.-A. Tanaka}, Tokyo J. Math. 37, No. 1, 211--223 (2014; Zbl 1303.11083) Full Text: DOI Euclid OpenURL
Zorin, Evgeniy Multiplicity estimates for algebraically dependent analytic functions. (English) Zbl 1294.11121 Proc. Lond. Math. Soc. (3) 108, No. 4, 989-1029 (2014). Reviewer: Michel Waldschmidt (Paris) MSC: 11J81 11J82 11J61 11J93 11S82 11T55 PDF BibTeX XML Cite \textit{E. Zorin}, Proc. Lond. Math. Soc. (3) 108, No. 4, 989--1029 (2014; Zbl 1294.11121) Full Text: DOI arXiv OpenURL
Adamczewski, Boris The many faces of the Kempner number. (English) Zbl 1286.11109 J. Integer Seq. 16, No. 2, Article 13.2.15, 34 p. (2013). Reviewer: Jaroslav Hančl (Ostrava) MSC: 11J81 11J87 11J70 PDF BibTeX XML Cite \textit{B. Adamczewski}, J. Integer Seq. 16, No. 2, Article 13.2.15, 34 p. (2013; Zbl 1286.11109) Full Text: arXiv EMIS OpenURL
Bundschuh, Peter; Väänänen, Keijo Algebraic independence of the generating functions of Stern’s sequence and of its twist. (English) Zbl 1268.11096 J. Théor. Nombres Bordx. 25, No. 1, 43-57 (2013). Reviewer: Michel Waldschmidt (Paris) MSC: 11J81 11J82 PDF BibTeX XML Cite \textit{P. Bundschuh} and \textit{K. Väänänen}, J. Théor. Nombres Bordx. 25, No. 1, 43--57 (2013; Zbl 1268.11096) Full Text: DOI Numdam Link OpenURL
Zorin, Evgeniy Zero order estimates for analytic functions. (English) Zbl 1264.11062 Int. J. Number Theory 9, No. 2, 333-392 (2013). Reviewer: Peter Bundschuh (Köln) MSC: 11J81 11J82 11J61 PDF BibTeX XML Cite \textit{E. Zorin}, Int. J. Number Theory 9, No. 2, 333--392 (2013; Zbl 1264.11062) 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
Tanaka, Taka-aki Algebraic independence properties related to certain infinite products. (English) Zbl 1284.11103 Amou, Masaaki, (ed.) et al., Diophantine analysis and related fields 2011, DARF–2011. Proceedings of the conference, Musashino, Tokyo, Japan, March 3–5, 2011. Melville, NY: American Institute of Physics (AIP) (ISBN 978-0-7354-0947-7/pbk). AIP Conference Proceedings 1385, 116-123 (2011). Reviewer: Jaroslav Hančl (Ostrava) MSC: 11J81 11J85 PDF BibTeX XML Cite \textit{T.-a. Tanaka}, AIP Conf. Proc. 1385, 116--123 (2011; Zbl 1284.11103) Full Text: DOI OpenURL
Kurosawa, Takeshi Transcendence criterion for values of certain functions of several variables. (English) Zbl 1201.11076 Result. Math. 57, No. 1-2, 1-22 (2010). Reviewer: Zhu Yaochen (Beijing) MSC: 11J81 11J91 PDF BibTeX XML Cite \textit{T. Kurosawa}, Result. Math. 57, No. 1--2, 1--22 (2010; Zbl 1201.11076) Full Text: DOI OpenURL
Adamczewski, Boris Non-converging continued fractions related to the Stern diatomic sequence. (English) Zbl 1210.11077 Acta Arith. 142, No. 1, 67-78 (2010). Reviewer: Takao Komatsu (Hirosaki) MSC: 11J70 11J81 11B83 PDF BibTeX XML Cite \textit{B. Adamczewski}, Acta Arith. 142, No. 1, 67--78 (2010; Zbl 1210.11077) Full Text: DOI OpenURL
Coons, Michael The transcendence of series related to Stern’s diatomic sequence. (English) Zbl 1250.11015 Int. J. Number Theory 6, No. 1, 211-217 (2010). Reviewer: Maciej Ulas (Kraków) MSC: 11B37 11B83 11J91 PDF BibTeX XML Cite \textit{M. Coons}, Int. J. Number Theory 6, No. 1, 211--217 (2010; Zbl 1250.11015) Full Text: DOI OpenURL
Dilcher, Karl; Stolarsky, Kenneth B. Stern polynomials and double-limit continued fractions. (English) Zbl 1250.11016 Acta Arith. 140, No. 2, 119-134 (2009). Reviewer: Michael Coons (Callaghan) MSC: 11B37 11B75 11B83 11J70 PDF BibTeX XML Cite \textit{K. Dilcher} and \textit{K. B. Stolarsky}, Acta Arith. 140, No. 2, 119--134 (2009; Zbl 1250.11016) Full Text: DOI OpenURL
Tanaka, Taka-aki Conditions for the algebraic independence of certain series involving continued fractions and generated by linear recurrences. (English) Zbl 1198.11062 J. Number Theory 129, No. 12, 3081-3093 (2009). Reviewer: Takao Komatsu (Hirosaki) MSC: 11J70 11J85 PDF BibTeX XML Cite \textit{T.-a. Tanaka}, J. Number Theory 129, No. 12, 3081--3093 (2009; Zbl 1198.11062) Full Text: DOI OpenURL
Bombieri, Enrico Problems and results on the distribution of algebraic points on algebraic varieties. (English) Zbl 1194.11070 J. Théor. Nombres Bordx. 21, No. 1, 41-57 (2009). Reviewer: Michel Waldschmidt (Paris) MSC: 11G35 11G50 14G25 14G05 PDF BibTeX XML Cite \textit{E. Bombieri}, J. Théor. Nombres Bordx. 21, No. 1, 41--57 (2009; Zbl 1194.11070) Full Text: DOI EuDML Link OpenURL
Waldschmidt, Michel Words and transcendence. (English) Zbl 1195.11095 Chen, W. W. L. (ed.) et al., Analytic number theory. Essays in honour of Klaus Roth on the occasion of his 80th birthday. Cambridge: Cambridge University Press (ISBN 978-0-521-51538-2/hbk). 449-470 (2009). Reviewer: Jean-Paul Allouche (Orsay) MSC: 11J81 11J82 11J87 11B85 68R15 PDF BibTeX XML Cite \textit{M. Waldschmidt}, in: Analytic number theory. Essays in honour of Klaus Roth on the occasion of his 80th birthday. Cambridge: Cambridge University Press. 449--470 (2009; Zbl 1195.11095) Full Text: arXiv OpenURL
Pellarin, Federico Aspects of algebraic independence in non-zero characteristic (after Anderson, Brownawell, Denis, Papanikolas, Thakur, Yu, et al.). (Aspects de l’indépendance algébrique en caractéristique non nulle (d’après Anderson, Brownawell, Denis, Papanikolas, Thakur, Yu, et al.).) (French) Zbl 1185.11048 Séminaire Bourbaki. Volume 2006/2007. Exposés 967–981. Paris: Société Mathématique de France (ISBN 978-2-85629-253-2/pbk). Astérisque 317, 205-242, Exp. No. 973 (2008). Reviewer: Michel Waldschmidt (Paris) MSC: 11J93 11J85 11G09 12H10 PDF BibTeX XML Cite \textit{F. Pellarin}, Astérisque 317, 205--242, Exp. No. 973 (2008; Zbl 1185.11048) Full Text: Link OpenURL
Tanaka, Taka-aki Remarkable algebraic independence property of certain series related to continued fractions. (English) Zbl 1144.11058 Komatsu, Takao (ed.), Diophantine analysis and related fields, DARF 2007/2008. Proceedings of the conferences, Yokohama, Japan, March 7–9, 2007 and Kyoto, Japan, March 5–7, 2008. Melville, NY: American Institute of Physics (AIP) (ISBN 978-0-7354-0495-3). AIP Conference Proceedings 976, 190-204 (2008). Reviewer: John H. Loxton (Greenwich) MSC: 11J85 11B39 11J70 PDF BibTeX XML Cite \textit{T.-a. Tanaka}, AIP Conf. Proc. 976, 190--204 (2008; Zbl 1144.11058) Full Text: DOI OpenURL
Dubickas, Arturas On the discriminant of the power of an algebraic number. (English) Zbl 1127.11069 Stud. Sci. Math. Hung. 44, No. 1, 27-34 (2007). MSC: 11R04 11R29 11J68 11J86 PDF BibTeX XML Cite \textit{A. Dubickas}, Stud. Sci. Math. Hung. 44, No. 1, 27--34 (2007; Zbl 1127.11069) Full Text: DOI OpenURL
Tachiya, Yohei Transcendence of certain infinite products. (English) Zbl 1116.11053 J. Number Theory 125, No. 1, 182-200 (2007). Reviewer: Michel Waldschmidt (Paris) MSC: 11J81 PDF BibTeX XML Cite \textit{Y. Tachiya}, J. Number Theory 125, No. 1, 182--200 (2007; Zbl 1116.11053) Full Text: DOI OpenURL
Denis, Laurent Algebraic independence of logarithms in characteristic \(p\). (Indépendance algébrique de logarithmes en caractéristique \(p\).) (French) Zbl 1116.11058 Bull. Aust. Math. Soc. 74, No. 3, 461-470 (2006). Reviewer: Andreas Schweizer (Exeter) MSC: 11J93 11G09 11J85 PDF BibTeX XML Cite \textit{L. Denis}, Bull. Aust. Math. Soc. 74, No. 3, 461--470 (2006; Zbl 1116.11058) Full Text: DOI OpenURL
Tanaka, Taka-aki Algebraic independence of power series generated by linearly independent positive numbers. (English) Zbl 1074.11037 Result. Math. 46, No. 3-4, 367-380 (2004). Reviewer: Jaroslav Hančl (Ostrava) MSC: 11J81 PDF BibTeX XML Cite \textit{T.-a. Tanaka}, Result. Math. 46, No. 3--4, 367--380 (2004; Zbl 1074.11037) Full Text: DOI OpenURL
Duverney, Daniel; Nishioka, Kumiko An inductive method for proving the transcendence of certain series. (English) Zbl 1049.11078 Acta Arith. 110, No. 4, 305-330 (2003). Reviewer: Peter Bundschuh (Köln) MSC: 11J81 PDF BibTeX XML Cite \textit{D. Duverney} and \textit{K. Nishioka}, Acta Arith. 110, No. 4, 305--330 (2003; Zbl 1049.11078) Full Text: DOI OpenURL
Kurosawa, Takeshi; Shiokawa, Iekata \(q\)-linear functions and algebraic independence. (English) Zbl 1100.11022 Tokyo J. Math. 25, No. 2, 459-472 (2002). Reviewer: François Gramain (Saint-Etienne) MSC: 11J85 11A63 PDF BibTeX XML Cite \textit{T. Kurosawa} and \textit{I. Shiokawa}, Tokyo J. Math. 25, No. 2, 459--472 (2002; Zbl 1100.11022) Full Text: DOI OpenURL
Tanaka, Taka-aki Transcendence of the values of certain series with Hadamard’s gaps. (English) Zbl 0998.11037 Arch. Math. 78, No. 3, 202-209 (2002). Reviewer: Peter Bundschuh (Köln) MSC: 11J81 PDF BibTeX XML Cite \textit{T.-a. Tanaka}, Arch. Math. 78, No. 3, 202--209 (2002; Zbl 0998.11037) Full Text: DOI OpenURL
Nishioka, Kumiko Algebraic independence of Fredholm series. (English) Zbl 0991.11042 Acta Arith. 100, No. 4, 315-327 (2001). Reviewer: Peter Bundschuh (Köln) MSC: 11J81 PDF BibTeX XML Cite \textit{K. Nishioka}, Acta Arith. 100, No. 4, 315--327 (2001; Zbl 0991.11042) Full Text: DOI OpenURL
Duverney, Daniel Irrationality of fast converging series of rational numbers. (English) Zbl 1002.11060 J. Math. Sci., Tokyo 8, No. 2, 275-316 (2001). Reviewer: John H.Loxton (North Ryde) MSC: 11J72 11J82 PDF BibTeX XML Cite \textit{D. Duverney}, J. Math. Sci., Tokyo 8, No. 2, 275--316 (2001; Zbl 1002.11060) OpenURL
Waldschmidt, Michel Half a century of transcendence. (Un demi-siècle de transcendance.) (French) Zbl 0977.11030 Pier, Jean-Paul (ed.), Development of mathematics 1950-2000. Basel: Birkhäuser. 1121-1186 (2000). Reviewer: Maurice Mignotte (Strasbourg) MSC: 11Jxx 11-02 11-03 11Dxx PDF BibTeX XML Cite \textit{M. Waldschmidt}, in: Development of mathematics 1950--2000. Basel: Birk\-häu\-ser. 1121--1186 (2000; Zbl 0977.11030) OpenURL
Denis, Laurent Algebraic independence of the derivatives of a period of the Carlitz module. (Indépendance algébrique des dérivées d’une période du module de Carlitz.) (French) Zbl 0961.11020 J. Aust. Math. Soc., Ser. A 69, No. 1, 8-18 (2000). Reviewer: Ulrich Tipp (Bochum) MSC: 11G09 11J85 11J93 PDF BibTeX XML Cite \textit{L. Denis}, J. Aust. Math. Soc., Ser. A 69, No. 1, 8--18 (2000; Zbl 0961.11020) OpenURL
Chirskiĭ, V. G. Linear independence of the \(p\)-adic values of certain \(q\)-basic hypergeometric series. (Russian. English summary) Zbl 0979.11038 Fundam. Prikl. Mat. 5, No. 2, 619-625 (1999). Reviewer: Jaroslav Hančl (Ostrava) MSC: 11J72 PDF BibTeX XML Cite \textit{V. G. Chirskiĭ}, Fundam. Prikl. Mat. 5, No. 2, 619--625 (1999; Zbl 0979.11038) Full Text: Link OpenURL
Gramain, François Transcendence and modular functions. (Transcendence et fonctions modulaires.) (French) Zbl 0959.11034 J. Théor. Nombres Bordx. 11, No. 1, 73-90 (1999). Reviewer: Michael Waldschmidt (Paris) MSC: 11J91 PDF BibTeX XML Cite \textit{F. Gramain}, J. Théor. Nombres Bordx. 11, No. 1, 73--90 (1999; Zbl 0959.11034) Full Text: DOI Numdam EuDML EMIS OpenURL
Masser, D. W. Algebraic independence properties of the Hecke-Mahler series. (English) Zbl 0929.11021 Q. J. Math., Oxf. II. Ser. 50, No. 198, 207-230 (1999). Reviewer: J.H.Loxton (North Ryde) MSC: 11J85 PDF BibTeX XML Cite \textit{D. W. Masser}, Q. J. Math., Oxf. II. Ser. 50, No. 198, 207--230 (1999; Zbl 0929.11021) Full Text: DOI OpenURL
Amou, Masaaki; Katsurada, Masanori Irrationality results for values of generalized Tschakaloff series. (English) Zbl 0929.11020 J. Number Theory 77, No. 1, 155-169 (1999). Reviewer: J.H.Loxton (North Ryde) MSC: 11J82 PDF BibTeX XML Cite \textit{M. Amou} and \textit{M. Katsurada}, J. Number Theory 77, No. 1, 155--169 (1999; Zbl 0929.11020) Full Text: DOI OpenURL
Tanaka, Taka-aki Algebraic independence results related to linear recurrences. (English) Zbl 0946.11015 Osaka J. Math. 36, No. 1, 203-227 (1999). Reviewer: F.Gramain (Saint-Etienne) MSC: 11J85 11J81 11B37 11B39 PDF BibTeX XML Cite \textit{T.-a. Tanaka}, Osaka J. Math. 36, No. 1, 203--227 (1999; Zbl 0946.11015) OpenURL
Tanaka, Taka-aki Algebraic independence results related to linear recurrences. (English) Zbl 1069.11506 Son, Jin-Woo (ed.) et al., Transcendental number theory and related topics. Proceedings of the Japan-Korea joint seminar, Masan, Republic of Korea, November 24–25, 1997. Masan: Kyungnam University, Basic Sciences Research Institute. 47-81 (1998). MSC: 11J85 11J81 11B37 PDF BibTeX XML Cite \textit{T.-a. Tanaka}, in: Transcendental number theory and related topics. Proceedings of the Japan-Korea joint seminar, Masan, Republic of Korea, November 24--25, 1997. Masan: Kyungnam University, Basic Sciences Research Institute. 47--81 (1998; Zbl 1069.11506) OpenURL
Tenba, Masaaki Introduction to transcendental numbers: proof of the Mahler-Manin conjecture. (Japanese) Zbl 0961.11023 Seminar on Mathematical Sciences. 26. Yokohama: Keio University, Department of Mathematics, viii, 47 p. (1998). Reviewer: Yin Linsheng (Guangzhou) MSC: 11J81 11J89 11-02 11J91 11J85 11K60 11J25 11J72 PDF BibTeX XML Cite \textit{M. Tenba}, Introduction to transcendental numbers: proof of the Mahler-Manin conjecture (Japanese). Yokohama: Keio University, Department of Mathematics (1998; Zbl 0961.11023) OpenURL
Philippon, Patrice Algebraic independence and \(K\)-functions. (Indépendance algébrique et \(K\)-fonctions.) (French) Zbl 0887.11032 J. Reine Angew. Math. 497, 1-15 (1998). Reviewer: P.Philippon (Paris) MSC: 11J85 11J91 11J82 PDF BibTeX XML Cite \textit{P. Philippon}, J. Reine Angew. Math. 497, 1--15 (1998; Zbl 0887.11032) Full Text: DOI OpenURL
Amoroso, Francesco Algebraic numbers close to 1: Results and methods. (English) Zbl 0892.11023 Murty, V. Kumar (ed.) et al., Number theory. Proceedings of the international conference on discrete mathematics and number theory, Tiruchirapalli, India, January 3–6, 1996 on the occasion of the 10th anniversary of the Ramanujan Mathematical Society. Providence, RI: American Mathematical Society. Contemp. Math. 210, 305-316 (1998). Reviewer: Daniel Duverney (Lille) MSC: 11J68 11J85 PDF BibTeX XML Cite \textit{F. Amoroso}, Contemp. Math. 210, 305--316 (1998; Zbl 0892.11023) OpenURL
Duverney, Daniel On arithmetic properties of Tschakaloff’s function. (Sur les propriétés arithmétiques de la fonction de Tschakaloff.) (French) Zbl 0923.11104 Period. Math. Hung. 35, No. 3, 149-157 (1997). MSC: 11J72 11J91 PDF BibTeX XML Cite \textit{D. Duverney}, Period. Math. Hung. 35, No. 3, 149--157 (1997; Zbl 0923.11104) Full Text: DOI OpenURL
Chirskiĭ, V. G. On the algebraic independence of the values of functions satisfying systems of functional equations. (English. Russian original) Zbl 0916.11041 Lupanov, O. B. (ed.), Analytic number theory and applications. Collected papers in honor of the sixtieth birthday of Professor Anatolii Alexeevich Karatsuba. Moscow: MAIK Nauka/Interperiodica Publishing, Proc. Steklov Inst. Math. 218, 433-438 (1997); translation from Tr. Mat. Inst. Steklova 218, 433-438 (1997). Reviewer: John H. Loxton (North Ryde) MSC: 11J85 11J91 PDF BibTeX XML Cite \textit{V. G. Chirskiĭ}, in: Analytic number theory and applications. Collected papers in honor of the sixtieth birthday of Professor Anatolii Alexeevich Karatsuba. Moscow: MAIK Nauka/Interperiodica Publishing. 433--438 (1997; Zbl 0916.11041); translation from Tr. Mat. Inst. Steklova 218, 433--438 (1997) OpenURL
Nishioka, Kumiko A new proof of Masser’s vanishing theorem. (English) Zbl 0874.11053 Proc. Am. Math. Soc. 124, No. 11, 3271-3274 (1996). Reviewer: J.H.Loxton (North Ryde) MSC: 11J91 11J81 PDF BibTeX XML Cite \textit{K. Nishioka}, Proc. Am. Math. Soc. 124, No. 11, 3271--3274 (1996; Zbl 0874.11053) Full Text: DOI OpenURL
Nishioka, Kumiko Mahler functions and transcendence. (English) Zbl 0876.11034 Lecture Notes in Mathematics. 1631. Berlin: Springer. viii, 185 p. (1996). Reviewer: J.H.Loxton (North Ryde) MSC: 11J81 11-02 11B85 11B83 11J85 PDF BibTeX XML Cite \textit{K. Nishioka}, Mahler functions and transcendence. Berlin: Springer (1996; Zbl 0876.11034) Full Text: DOI OpenURL
Philippon, Patrice New aspects of transcendence. (Nouveaux aspects de la transcendance.) (French) Zbl 0843.11035 J. Théor. Nombres Bordx. 7, No. 1, 191-218 (1995). Reviewer: P.Bundschuh (Köln) MSC: 11J81 11J85 11J86 PDF BibTeX XML Cite \textit{P. Philippon}, J. Théor. Nombres Bordx. 7, No. 1, 191--218 (1995; Zbl 0843.11035) Full Text: DOI Numdam EuDML EMIS OpenURL
Töpfer, Thomas Algebraic independence of the values of generalized Mahler functions. (English) Zbl 0815.11038 Acta Arith. 70, No. 2, 161-181 (1995). Reviewer: T.Töpfer (Köln) MSC: 11J82 11J91 PDF BibTeX XML Cite \textit{T. Töpfer}, Acta Arith. 70, No. 2, 161--181 (1995; Zbl 0815.11038) Full Text: DOI 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
Töpfer, Thomas An axiomatization of Nesterenko’s method and applications on Mahler functions. (English) Zbl 0813.11043 J. Number Theory 49, No. 1, 1-26 (1994). Reviewer: M.Waldschmidt (Paris) MSC: 11J85 11J91 PDF BibTeX XML Cite \textit{T. Töpfer}, J. Number Theory 49, No. 1, 1--26 (1994; Zbl 0813.11043) Full Text: DOI OpenURL
Nishioka, Kumiko Note on a paper by Mahler. (English) Zbl 0820.11044 Tsukuba J. Math. 17, No. 2, 455-459 (1993). Reviewer: J.H.Loxton (North Ryde) MSC: 11J91 PDF BibTeX XML Cite \textit{K. Nishioka}, Tsukuba J. Math. 17, No. 2, 455--459 (1993; Zbl 0820.11044) Full Text: DOI 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
Becker, Paul-Georg Transcendence of the values of functions satisfying generalized Mahler type functional equations. (English) Zbl 0770.11037 J. Reine Angew. Math. 440, 111-128 (1993). Reviewer: P.-G.Becker (Köln) MSC: 11J81 11J91 PDF BibTeX XML Cite \textit{P.-G. Becker}, J. Reine Angew. Math. 440, 111--128 (1993; Zbl 0770.11037) Full Text: DOI Crelle EuDML OpenURL
Amou, Masaaki An improvement of a transcendence measure of Galochkin and Mahler’s \(S\)- numbers. (English) Zbl 0766.11033 J. Aust. Math. Soc., Ser. A 52, No. 1, 130-140 (1992). Reviewer: K.Väänänen (Oulu) MSC: 11J82 PDF BibTeX XML Cite \textit{M. Amou}, J. Aust. Math. Soc., Ser. A 52, No. 1, 130--140 (1992; Zbl 0766.11033) OpenURL
Becker, Paul-Georg Algebraic independence of the values of certain series by Mahler’s method. (English) Zbl 0764.11029 Monatsh. Math. 114, No. 3-4, 183-198 (1992). Reviewer: P.-G.Becker (Köln) MSC: 11J85 11J81 PDF BibTeX XML Cite \textit{P.-G. Becker}, Monatsh. Math. 114, No. 3--4, 183--198 (1992; Zbl 0764.11029) Full Text: DOI EuDML OpenURL
Amou, Masaaki Algebraic independence of the values of certain functions at a transcendental number. (English) Zbl 0735.11031 Acta Arith. 59, No. 1, 71-82 (1991). Reviewer: P.Philippon (Paris) MSC: 11J82 11J85 PDF BibTeX XML Cite \textit{M. Amou}, Acta Arith. 59, No. 1, 71--82 (1991; Zbl 0735.11031) Full Text: DOI EuDML OpenURL
Becker, Paul-Georg Effective measures for algebraic independence of the values of Mahler type functions. (English) Zbl 0735.11030 Acta Arith. 58, No. 3, 239-250 (1991). Reviewer: P.Philippon (Paris) MSC: 11J82 11J85 PDF BibTeX XML Cite \textit{P.-G. Becker}, Acta Arith. 58, No. 3, 239--250 (1991; Zbl 0735.11030) Full Text: DOI EuDML OpenURL
Baker, Alan Transcendental number theory. Paperback ed. (English) Zbl 0715.11032 Cambridge Mathematical Library. Cambridge etc.: Cambridge University Press. x, 165 p. £10.95; $ 17.95 (1990). Reviewer: O.Ninnemann MSC: 11Jxx 11-01 01A75 11J81 11J86 11J85 11J89 11J83 11J68 11D41 11J91 11R29 11K60 11R11 PDF BibTeX XML Cite \textit{A. Baker}, Transcendental number theory. Paperback ed. Cambridge etc.: Cambridge University Press (1990; Zbl 0715.11032) OpenURL
Nishioka, Keiji; Nishioka, Kumiko Algebraic independence of elementary functions and its application to Masser’s vanishing theorem. (English) Zbl 0723.11033 Aequationes Math. 40, No. 1, 67-77 (1990). Reviewer: F.Gramain (Saint-Etienne) MSC: 11J85 11J81 12H05 11S80 PDF BibTeX XML Cite \textit{K. Nishioka} and \textit{K. Nishioka}, Aequationes Math. 40, No. 1, 67--77 (1990; Zbl 0723.11033) Full Text: DOI EuDML OpenURL
Wass, N. Ch. Algebraic independence of the values at algebraic points of a class of functions considered by Mahler. (English) Zbl 0707.11050 Diss. Math. 303, 1-61 (1990). Reviewer: Rolf Wallisser (Freiburg i. Br.) MSC: 11J85 PDF BibTeX XML Cite \textit{N. Ch. Wass}, Diss. Math. 303, 1--61 (1990; Zbl 0707.11050) OpenURL
Loxton, J. H.; van der Poorten, A. J. Arithmetic properties of automata: regular sequences. (English) Zbl 0656.10033 J. Reine Angew. Math. 392, 57-69 (1988). Reviewer: J.-P.Allouche MSC: 11J81 68Q70 11J85 11B99 PDF BibTeX XML Cite \textit{J. H. Loxton} and \textit{A. J. van der Poorten}, J. Reine Angew. Math. 392, 57--69 (1988; Zbl 0656.10033) Full Text: Crelle EuDML OpenURL
Loxton, J. H. Automata and transcendence. (English) Zbl 0656.10032 New advances in transcendence theory, Proc. Symp., Durham/UK 1986, 215-228 (1988). Reviewer: P.Liardet MSC: 11J81 68Q70 PDF BibTeX XML OpenURL
Nesterenko, Yu. V. Measures of algebraic independence of numbers and functions. (English) Zbl 0615.10043 Journées arithmétiques, Besançon/France 1985, Astérisque 147/148, 141-149 (1987). Reviewer: M.Waldschmidt MSC: 11J85 11J81 11-02 33B10 13B25 34A30 30D05 PDF BibTeX XML OpenURL
Nesterenko, Yu. V. On a measure of the algebraic independence of the values of the exponential function. (English. Russian original) Zbl 0608.10035 Sov. Math., Dokl. 33, 200-203 (1986); translation from Dokl. Akad. Nauk SSSR 286, 817-821 (1986). Reviewer: M.Waldschmidt MSC: 11J85 11J81 PDF BibTeX XML Cite \textit{Yu. V. Nesterenko}, Sov. Math., Dokl. 33, 200--203 (1986; Zbl 0608.10035); translation from Dokl. Akad. Nauk SSSR 286, 817--821 (1986) OpenURL
Molchanov, S. M. Estimates of transcendence measures in Mahler’s method. (Russian) Zbl 0645.10032 Diophantine approximations, 1, Collect. Artic., Moskva 1985, 56-65 (1985). Reviewer: Kunrui Yu (Beijing) MSC: 11J91 PDF BibTeX XML OpenURL
Becker-Landeck, P.-G. Quantitative results connected with Mahler’s transcencende method. (English) Zbl 0598.10041 Result. Math. 8, 92-93 (1985). Reviewer: O.Ninnemann MSC: 11J81 11J85 PDF BibTeX XML Cite \textit{P. G. Becker-Landeck}, Result. Math. 8, 92--93 (1985; Zbl 0598.10041) Full Text: DOI 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
Silverman, Joseph H. Integer points on curves of genus 1. (English) Zbl 0487.10015 J. Lond. Math. Soc., II. Ser. 28, 1-7 (1983). MSC: 11D25 14H52 PDF BibTeX XML Cite \textit{J. H. Silverman}, J. Lond. Math. Soc., II. Ser. 28, 1--7 (1983; Zbl 0487.10015) Full Text: DOI OpenURL
Schlickewei, Hans Peter \(p\)-adic \(T\)-numbers do exist. (English) Zbl 0465.10030 Acta Arith. 39, 181-191 (1981). MSC: 11J61 11J81 PDF BibTeX XML Cite \textit{H. P. Schlickewei}, Acta Arith. 39, 181--191 (1981; Zbl 0465.10030) Full Text: DOI EuDML OpenURL
Lekkerkerker, C. G. Geometry of numbers. (English) Zbl 0198.38002 Bibliotheca Mathematica. A Series of Monographs on Pure and Applied Mathematics 8. Amsterdam-London: North-Holland Publishing Company; Groningen: Wolters-Noordhoff Publishing. x, 510 p. (1969). Reviewer: Peter M. Gruber (Wien) MSC: 11Hxx 11-02 PDF BibTeX XML OpenURL