Boege, Tobias No eleventh conditional Ingleton inequality. (English) Zbl 07962384 Exp. Math. 33, No. 4, 808-816 (2024). MSC: 94A17 62R01 94-08 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
David, Sinnou; Hirata-Kohno, Noriko; Kawashima, Makoto Linear forms in polylogarithms. (English) Zbl 1504.11082 Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 23, No. 3, 1447-1490 (2022). Reviewer: Jaroslav Hančl (Ostrava) MSC: 11J72 11J82 11J61 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Galochkin, Alexander; Godunova, Anastasia On approximations of solutions of the equation \(P(z,\ln z) = 0\) by algebraic numbers. (English) Zbl 1456.11128 Mosc. J. Comb. Number Theory 9, No. 4, 435-440 (2020). Reviewer: Jaroslav Hančl (Ostrava) MSC: 11J82 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF Full Text: DOI
Bodnar, Taras; Dette, Holger; Parolya, Nestor Testing for independence of large dimensional vectors. (English) Zbl 1436.60018 Ann. Stat. 47, No. 5, 2977-3008 (2019). MSC: 60B20 15B52 60F05 62H15 62H20 62F05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Nguyen, Khoa D. Algebraic independence of local conjugacies and related questions in polynomial dynamics. (English) Zbl 1311.11068 Proc. Am. Math. Soc. 143, No. 4, 1491-1499 (2015). Reviewer: Jaroslav Hančl (Ostrava) MSC: 11J81 37F10 37P30 11J91 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Boxall, Gareth J.; Jones, Gareth O. Algebraic values of certain analytic functions. (English) Zbl 1388.11041 Int. Math. Res. Not. 2015, No. 4, 1141-1158 (2015). Reviewer: Michel Waldschmidt (Paris) MSC: 11J91 33B15 14G05 11G99 11J72 11J82 11M06 × Cite Format Result Cite Review PDF Full Text: DOI
Bundschuh, Peter; Väänänen, Keijo Transcendence results on the generating functions of the characteristic functions of certain self-generating sets. II. (English) Zbl 1379.11070 Acta Arith. 167, No. 3, 239-249 (2015). MSC: 11J81 11J82 11J91 12F20 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Murty, M. Ram; Rath, Purusottam Transcendental numbers. (English) Zbl 1297.11001 New York, NY: Springer (ISBN 978-1-4939-0831-8/pbk; 978-1-4939-0832-5/ebook). xiv, 217 p. (2014). Reviewer: Werner Kleinert (Berlin) MSC: 11-01 11J81 11J82 11J85 11J86 11J68 11J89 × Cite Format Result Cite Review PDF Full Text: DOI
Bundschuh, Peter; Väänänen, Keijo Transcendence results on the generating functions of the characteristic functions of certain self-generating sets. (English) Zbl 1292.11082 Acta Arith. 162, No. 3, 273-288 (2014). Reviewer: Jaroslav Hančl (Ostrava) MSC: 11J81 11J82 11J91 30B30 × Cite Format Result Cite Review PDF Full Text: DOI
Roy, Damien An effective version of the Lindemann-Weierstrass theorem using algebraic independence methods. (Une version effective du théorème de Lindemann-Weierstrass par des méthodes d’indépendance algébrique.) (French. English summary) Zbl 1320.11067 Enseign. Math. (2) 59, No. 3-4, 287-306 (2013). MSC: 11J85 11J82 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kholyavka, Ya. M. On a measure of algebraic independence of modulus and values of Jacobi elliptic function. (Ukrainian. English, Russian summaries) Zbl 1382.11047 Carpathian Math. Publ. 5, No. 1, 134-142 (2013). MSC: 11J82 11J89 × Cite Format Result Cite Review PDF Full Text: DOI
Bose, Arup; Sen, Sanchayan Finite diagonal random matrices. (English) Zbl 1278.82027 J. Theor. Probab. 26, No. 3, 819-835 (2013). MSC: 82B41 60B20 60B10 46L53 46L54 15B52 15A18 × Cite Format Result Cite Review PDF Full Text: DOI
Uhler, Caroline; Raskutti, Garvesh; Bühlmann, Peter; Yu, Bin Geometry of the faithfulness assumption in causal inference. (English) Zbl 1267.62068 Ann. Stat. 41, No. 2, 436-463 (2013). MSC: 62H05 05C20 65C60 62H20 05C90 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
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 × Cite Format Result Cite Review PDF Full Text: DOI Numdam
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 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Zorin, Evgeniy Algebraic independence and normality of the values of Mahler’s functions. arXiv:1309.0105 Preprint, arXiv:1309.0105 [math.NT] (2013). MSC: 11J91 11J82 11J85 × Cite Format Result Cite Full Text: arXiv OA License
Rivoal, T. On the arithmetic nature of the values of the gamma function, Euler’s constant, and Gompertz’s constant. (English) Zbl 1288.11073 Mich. Math. J. 61, No. 2, 239-254 (2012). Reviewer: Michel Waldschmidt (Paris) MSC: 11J91 11J13 11J82 33B15 × Cite Format Result Cite Review PDF Full Text: DOI Euclid
Waldschmidt, Michel Recent advances in Diophantine approximation. (English) Zbl 1271.11070 Goldfeld, Dorian (ed.) et al., Number theory, analysis and geometry. In memory of Serge Lang. Berlin: Springer (ISBN 978-1-4614-1259-5/hbk; 978-1-4614-1260-1/ebook). 659-704 (2012). Reviewer: Peter Bundschuh (Köln) MSC: 11Jxx 11J04 11J13 11J82 11J83 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Denis, Laurent Algebraic approximation in characteristic \(p\). (Approximation algébrique en caractéristique \(p\).) (French) Zbl 1231.11084 Acta Arith. 147, No. 2, 101-113 (2011). Reviewer: Michel Waldschmidt (Paris) MSC: 11J93 11G09 11J85 × Cite Format Result Cite Review PDF Full Text: DOI
Rałowski, Robert Nonmeasurability in Banach spaces. (English) Zbl 1189.03069 Far East J. Math. Sci. (FJMS) 36, No. 2, 125-131 (2010). MSC: 03E75 03E35 28A05 46B03 46G12 × Cite Format Result Cite Review PDF Full Text: arXiv Link
Nesterenko, Yu. V. Algebraic independence. (English) Zbl 1217.11071 Lectures on Mathematics and Physics. Mathematics. Tata Institute of Fundamental Research 90. New Delhi: Narosa Publishing House/Published for the Tata Institute of Fundamental Research (ISBN 978-81-7319-984-4/hbk). viii, 162 p. (2009). Reviewer: Peter Bundschuh (Köln) MSC: 11J85 11-02 11J81 11J82 × Cite Format Result Cite Review PDF
Waldschmidt, Michel Elliptic functions and transcendence. (English) Zbl 1210.11084 Alladi, Krishnaswami (ed.), Surveys in number theory. New York, NY: Springer (ISBN 978-0-387-78509-7/hbk). Developments in Mathematics 17, 1-46 (2008). MSC: 11J89 11-02 11J82 × Cite Format Result Cite Review PDF Full Text: DOI HAL
Gaudron, Éric Study of the rational case of the theory of linear forms in logarithms. (English) Zbl 1197.11085 J. Number Theory 127, No. 2, 220-261 (2007). MSC: 11J86 11J61 11J13 × Cite Format Result Cite Review PDF Full Text: DOI arXiv HAL
Schmidt, Wolfgang M. Diophantine approximation by algebraic hypersurfaces and varieties. (English) Zbl 1115.11037 Trans. Am. Math. Soc. 359, No. 5, 2221-2241 (2007). Reviewer: Michel Waldschmidt (Paris) MSC: 11J13 11J81 11J82 11J85 × Cite Format Result Cite Review PDF Full Text: DOI
Wang, Tianqin; Xu, Guangshan \(p\)-adic measures of algebraic independence for the values of Ramanujan functions and Klein modular functions. (English) Zbl 1117.11038 Acta Math. Sin., Engl. Ser. 23, No. 1, 83-88 (2007). Reviewer: François Gramain (Saint-Etienne) MSC: 11J61 11J82 11J91 × Cite Format Result Cite Review PDF Full Text: DOI
Elsner, C. On certain solutions of universal differential equations in algebraic points. (Über gewisse Lösungen universeller Differentialgleichungen in algebraischen Punkten.) (German. English summary) Zbl 1161.11023 Schwarz, Wolfgang (ed.) et al., Elementare und analytische Zahlentheorie. Tagungsband. Stuttgart: Franz Steiner Verlag (ISBN 3-515-08757-5/hbk). Schriften der Wissenschaftlichen Gesellschaft an der Johann-Wolfgang-Goethe-Universität Frankfurt am Main 20, 44-56 (2006). Reviewer: Rolf Wallisser (Freiburg i. Br.) MSC: 11J82 11J72 11J81 34A09 × Cite Format Result Cite Review PDF
Schmidt, Wolfgang M. Mahler and Koksma classification of points in \(\mathbb R^n\) and \(\mathbb C^n\). (English) Zbl 1192.11042 Funct. Approximatio, Comment. Math. 35, 307-319 (2006). Reviewer: Simon Kristensen (Aarhus) MSC: 11J82 11J83 × Cite Format Result Cite Review PDF Full Text: DOI Euclid
Waldschmidt, Michel Transcendence of periods: the state of the art. (English) Zbl 1220.11090 Pure Appl. Math. Q. 2, No. 2, 435-463 (2006). MSC: 11J81 11G15 11-02 11G18 11J86 11J89 11J95 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF Full Text: DOI
Takeuchi, Mamoru Quantitative results of algebraic independence and Baker’s method. (English) Zbl 1081.11052 Acta Arith. 119, No. 3, 211-241 (2005). Reviewer: Michel Waldschmidt (Paris) MSC: 11J89 11J82 11J85 11J86 × Cite Format Result Cite Review PDF Full Text: DOI
Xu, Guangshan; Wang, Tianqin \(p\)-adic measures for algebraic independence of the values of Mahler type functions. (Chinese. English summary) Zbl 1137.11329 Acta Math. Sin. 47, No. 5, 921-930 (2004). Reviewer: Zhu Yaochen (Beijing) MSC: 11J82 11J85 11J91 × Cite Format Result Cite Review PDF
Hart, Klaas Pieter An algebraic and logical approach to continuous images. (English) Zbl 1169.54354 Acta Univ. Carol., Math. Phys. 43, No. 2, 5-25 (2002). MSC: 54F15 03C50 03C98 03E55 03E65 06D05 06E15 28A60 54A35 54C10 54D40 54D80 54F45 54H10 × Cite Format Result Cite Review PDF Full Text: arXiv EuDML
Grinspan, Pierre Measures of simultaneous approximation for quasi-periods of Abelian varieties. (English) Zbl 1030.11033 J. Number Theory 94, No. 1, 136-176 (2002). Reviewer: Damien Roy (Ottawa / Ontario) MSC: 11J95 11J82 × Cite Format Result Cite Review PDF Full Text: DOI Link
Nopper, Thomas Meromorphic functions with arithmetic conditions and applications to irrationality. (Meromorphe Funktionen mit arithmetischen Bedingungen und Anwendungen auf Irrationalität.) (German) Zbl 0992.11045 Freiburg i. Br.: Univ. Freiburg, Mathematische Fakultät, 113 S. (2001). Reviewer: Peter Bundschuh (Köln) MSC: 11J72 11J82 × Cite Format Result Cite Review PDF
Roy, Damien Simultaneous algebraic approximation of Liouville numbers. (Approximation algébrique simultanée de nombres de Liouville.) (French) Zbl 0982.11041 Can. Math. Bull. 44, No. 1, 115-120 (2001). Reviewer: P.Philippon (Paris) MSC: 11J82 11J85 × Cite Format Result Cite Review PDF Full Text: DOI
Laurent, Michel; Roy, Damien Criteria of algebraic independence with multiplicities and approximation by surfaces. (English) Zbl 0990.11047 J. Reine Angew. Math. 536, 65-114 (2001). Reviewer: M.Laurent (Marseille), D.Roy (Ottawa) MSC: 11J85 11J82 × Cite Format Result Cite Review PDF Full Text: DOI
Roy, Damien An arithmetic criterion for the values of the exponential function. (English) Zbl 0981.11025 Acta Arith. 97, No. 2, 183-194 (2001). Reviewer: John H.Loxton (North Ryde) MSC: 11J82 11J85 × Cite Format Result Cite Review PDF Full Text: DOI
Bilu, Yuri; Bugeaud, Yann Proof of the Baker-Feldman theorem via linear forms in two logarithms. (Démonstration du théorème de Baker-Feldman via les formes linéaires en deux logarithmes.) (French) Zbl 1010.11036 J. Théor. Nombres Bordx. 12, No. 1, 13-23 (2000). Reviewer: Michel Waldschmidt (Paris) MSC: 11J68 11J86 × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML
Elsner, C. On an effective construction of large sets of algebraically independent numbers. (Über eine effektive Konstruktion großer Mengen algebraisch unabhängiger Zahlen.) (English) Zbl 0989.11037 Math. Semesterber. 47, No. 2, 243-256 (2000). Reviewer: Peter Bundschuh (Köln) MSC: 11J85 × Cite Format Result Cite Review PDF Full Text: DOI
Waldschmidt, Michel Conjectures for large transcendence degree. (English) Zbl 0962.11028 Halter-Koch, Franz (ed.) et al., Algebraic number theory and diophantine analysis. Proceedings of the international conference, Graz, Austria, August 30-September 5, 1998. Berlin: Walter de Gruyter. 497-520 (2000). Reviewer: Peter Bundschuh (Köln) MSC: 11J82 11J85 × Cite Format Result Cite Review PDF
Greuel, Bernd Algebraic independence of the values of Mahler functions satisfying implicit functional equations. (English) Zbl 0961.11024 Acta Arith. 93, No. 1, 1-20 (2000). Reviewer: John H.Loxton (North Ryde) MSC: 11J82 11J85 11J91 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Waldschmidt, Michel Diophantine approximation on linear algebraic groups. Transcendence properties of the exponential function in several variables. (English) Zbl 0944.11024 Grundlehren der Mathematischen Wissenschaften. 326. Berlin: Springer. xxiii, 633 p. (2000). Reviewer: P.Bundschuh (Köln) MSC: 11J81 11-02 20G15 20G30 × Cite Format Result Cite Review PDF Backlinks: MO
Bundschuh, Peter; Shiue, Peter Jau-Shyong; Yu, Xiuyuan Transcendence and algebraic independence connected with Mahler type numbers. (English) Zbl 0999.11038 Publ. Math. Debr. 56, No. 1-2, 121-130 (2000). Reviewer: Attila Pethő (Debrecen) MSC: 11J72 11J82 11J85 × Cite Format Result Cite Review PDF
Philippon, Patrice Algebraic approximations of points in projective spaces. I. (Approximations algébriques des points dans les espaces projectifs. I.) (French) Zbl 1096.11504 J. Number Theory 81, No. 2, 234-253 (2000). MSC: 11J82 11J85 × Cite Format Result Cite Review PDF Full Text: DOI
Greuel, Bernd Investigations on the algebraic independence of values of functions of Mahler type. (Untersuchungen zur algebraischen Unabhängigkeit der Werte von Funktionen vom Mahlerschen Typ.) (German) Zbl 1109.11317 Köln: Univ. Köln, Mathematisch-Naturwissenschaftliche Fakultät. 90 S. (1999). MSC: 11J85 11J91 30D05 11J82 × Cite Format Result Cite Review PDF Full Text: Link
Philippon, Patrice Measures of approximation of values of analytic functions. (Mesures d’approximation de valeurs de fonctions analytiques.) (French) Zbl 0938.11038 Acta Arith. 88, No. 2, 113-127 (1999). Reviewer: Jürgen Wolfart (Frankfurt /Main) MSC: 11J82 11J89 11J91 11J85 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Sert, Alain An effective version of the Lindemann-Weierstrass theorem for interpolation determinants. (Une version effective du théorème de Lindemann-Weierstrass par les déterminants d’interpolation.) (French) Zbl 0935.11024 J. Number Theory 76, No. 1, 94-119 (1999). Reviewer: F.Gramain (Saint-Etienne) MSC: 11J85 11J82 × Cite Format Result Cite Review PDF Full Text: DOI
Chudnovsky, D. V.; Chudnovsky, G. V. Classification of hypergeometric identities for \(\pi\) and other logarithms of algebraic numbers. (English) Zbl 0966.11050 Proc. Natl. Acad. Sci. USA 95, No. 6, 2744-2749 (1998). Reviewer: D.Duverney (Lille) MSC: 11Y60 33C20 11J82 × Cite Format Result Cite Review PDF Full Text: DOI Link
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 × Cite Format Result Cite Review PDF Full Text: DOI
Fel’dman, N. I.; Nesterenko, Yu. V. Parshin, A. N. (ed.); Shafarevich, I. R. (ed.); Gamkrelidze, R. V. (ed.) Number theory IV: Transcendental numbers. Edited by A. N. Parshin, I. R. Shafarevich and R. V. Gamkrelidze. Transl. from the Russian by Neal Koblitz. (English) Zbl 0885.11004 Encyclopaedia of Mathematical Sciences 44. Berlin: Springer (ISBN 3-540-61467-2/hbk). 345 p. (1998). Reviewer: M.Waldschmidt (Paris) MSC: 11-02 11J81 11J82 11J86 11J25 11J85 11J89 11J68 × Cite Format Result Cite Review PDF
Nesterenko, Yu. V. On the measure of algebraic independence of the values of Ramanujan functions. (English. Russian original) Zbl 0913.11030 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, 294-331 (1997); translation from Tr. Mat. Inst. Steklova 218, 299-334 (1997). Reviewer: M.Waldschmidt (Paris) MSC: 11J91 11J85 11J82 11F11 × Cite Format Result Cite Review PDF
Yanchenko, A. Ya. On the measure of algebraic independence of values of derivatives of a \(p\)-adic modular function. (English. Russian original) Zbl 0918.11041 Math. Notes 61, No. 3, 352-359 (1997); translation from Mat. Zametki 61, No. 3, 431-440 (1997). Reviewer: Jürgen Wolfart (Frankfurt am Main) MSC: 11J82 11J85 11F85 11F11 × Cite Format Result Cite Review PDF Full Text: DOI
Roy, Damien; Waldschmidt, Michel Simultaneous approximation and algebraic independence. (English) Zbl 0916.11042 Ramanujan J. 1, No. 4, 379-430 (1997). Reviewer: Guy Diaz (Saint-Etienne) MSC: 11J85 11J82 11J89 11J91 × Cite Format Result Cite Review PDF Full Text: DOI
Caveny, Deanna M. Commutative algebraic groups and refinements of the Gelfond-Feldman measure. (English) Zbl 0879.11039 Rocky Mt. J. Math. 26, No. 3, 889-935 (1996). Reviewer: M.Waldschmidt (Paris) MSC: 11J85 11J81 11J82 14L10 × Cite Format Result Cite Review PDF Full Text: DOI Link
Müller, Ralf Arithmetic studies in non-archimedean valued fields. (Arithmetische Untersuchungen in nicht-archimedisch bewerteten Körpern.) (German) Zbl 0855.11035 Köln: Univ. Köln, Math.-Naturwiss. Fak. 103 S. (1995). Reviewer: M.Waldschmidt (Paris) MSC: 11J61 12J25 46S10 11G09 11J82 × Cite Format Result Cite Review PDF
Zudilin, V. V. On rational approximations of values of a certain class of entire functions. (English. Russian original) Zbl 0848.11031 Sb. Math. 186, No. 4, 555-590 (1995); translation from Mat. Sb. 186, No. 4, 89-124 (1995). Reviewer: Xu Guangshan (Beijing) MSC: 11J82 11J91 11J85 34M99 30D15 × Cite Format Result Cite Review PDF Full Text: DOI
Komatsu, Takao Results on fractional parts of linear functions of \(n\) and applications to Beatty sequences. (English) Zbl 0891.11011 Bull. Aust. Math. Soc. 52, No. 2, 349-351 (1995). MSC: 11B83 11J70 11A55 11J82 11J85 11J91 × Cite Format Result Cite Review PDF Full Text: DOI
Xu, Guangshan On arithmetic properties of the values of Siegel’s \(E\) and \(G\) functions. (Chinese. English summary) Zbl 0846.11043 Adv. Math., Beijing 24, No. 2, 97-110 (1995). Reviewer: Zhu Yaochen (Beijing) MSC: 11J91 11-02 × Cite Format Result Cite Review PDF
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 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Ably, Mohammed A quantitative version of the Lindemann-Weierstrass theorem. (Une version quantitative du théorème de Lindemann-Weierstrass.) (French) Zbl 0813.11042 Acta Arith. 67, No. 1, 29-45 (1994). Reviewer: M.Waldschmidt (Paris) MSC: 11J85 11J82 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Töpfer, Thomas On the linear independence in algebraic number fields. (Über lineare Unabhängigkeit in algebraischen Zahlkörpern.) (German) Zbl 0804.11045 Result. Math. 25, No. 1-2, 139-152 (1994). Reviewer: K.Väänänen (Oulu) MSC: 11J82 11J72 × Cite Format Result Cite Review PDF Full Text: DOI
Caveny, Deanna M. Quantitative transcendence results for numbers associated with Liouville numbers. (English) Zbl 0802.11028 Proc. Am. Math. Soc. 120, No. 2, 349-357 (1994). Reviewer: M.Waldschmidt (Paris) MSC: 11J85 11J82 11J86 × Cite Format Result Cite Review PDF Full Text: DOI
Väänänen, K. On the approximation of certain infinite products. (English) Zbl 0818.11028 Math. Scand. 73, No. 2, 197-208 (1993). Reviewer: R.Wallisser (Freiburg i.Br.) MSC: 11J82 11J72 11J61 11J13 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Nguyen Tien Tai Effective estimates of the algebraic independence measures with respect to the field \(K\) for the values of \(\text{KE}\)-functions. (Vietnamese. English summary) Zbl 0940.11505 Tạp Chí Toán Học 21, No. 3-4, 35-45 (1993). MSC: 11J91 11J85 × Cite Format Result Cite Review PDF
Ably, Mohammed Quantitative results on algebraic independence for algebraic groups. (Résultats quantitatifs d’indépendance algébrique pour les groupes algébriques.) (French) Zbl 0758.11032 J. Number Theory 42, No. 2, 194-231 (1992). Reviewer: Michel Waldschmidt (Paris) MSC: 11J85 11J82 × Cite Format Result Cite Review PDF Full Text: DOI
Laohakosol, Vichian Dependence of arithmetic functions and Dirichlet series. (English) Zbl 0762.11001 Proc. Am. Math. Soc. 115, No. 3, 637-645 (1992). Reviewer: François Gramain (Saint-Etienne) MSC: 11J85 11J82 11M41 30B50 11A25 × Cite Format Result Cite Review PDF Full Text: DOI
Gorelov, V. A. Estimates for measures of algebraic independence of values of \(E\)- functions. (English. Russian original) Zbl 0808.11046 Russ. Math. 36, No. 10, 4-9 (1992); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1992, No. 10 (365) 6-11 (1992). Reviewer: Xu Guangshan (Beijing) MSC: 11J91 11J85 × Cite Format Result Cite Review PDF
Shestakov, S. O. Measure of algebraic independence of certain numbers. (Russian) Zbl 0769.11030 Vestn. Mosk. Univ., Ser. I 1992, No. 2, 8-12 (1992). Reviewer: Xu Guangshan (Beijing) MSC: 11J85 11J82 × Cite Format Result Cite Review PDF
Nishioka, Kumiko; Shiokawa, Iekata; Tamura, Jun-ichi Arithmetical properties of a certain power series. (English) Zbl 0770.11039 J. Number Theory 42, No. 1, 61-87 (1992). Reviewer: P.Bundschuh (Köln) MSC: 11J82 11J91 × Cite Format Result Cite Review PDF Full Text: DOI
Shestakov, S. O. On a measure of algebraic independence of certain numbers. (English. Russian original) Zbl 0784.11033 Mosc. Univ. Mech. Bull. 47, No. 2, 8-11 (1992); translation from Vestn. Mosk. Univ., Ser. I 1992, No. 2, 8-12 (1992). MSC: 11J85 11J82 × Cite Format Result Cite Review PDF
Nesterenko, Yuri V. On a measure of algebraic independence of the values of elliptic functions. (English) Zbl 0786.11047 Approximations diophantiennes et nombres transcendants, C.-R. Colloq., Luminy/Fr. 1990, 239-248 (1992). Reviewer: K.Väänänen (Oulu) MSC: 11J85 11J89 11J82 × Cite Format Result Cite Review PDF
Jabbouri, El Mostafa Sur un critère pour l’indépendance algébrique de P. Philippon. (On an algebraic independence criterion of P. Philippon). (French) Zbl 0777.11024 Approximations diophantiennes et nombres transcendants, C.-R. Colloq., Luminy/ Fr. 1990, 195-202 (1992). Reviewer: P.Philippon (Paris) MSC: 11J85 11J82 14Q20 × Cite Format Result Cite Review PDF
Nishioka, Kumiko Mahler’s functions and transcendental number – applications of Nesterenko’s theory. (Japanese) Zbl 0941.11505 Seminar on Mathematical Sciences 17. Yokohama: Keio University, Department of Mathematics. vi, 91 p. (1991). MSC: 11J91 × Cite Format Result Cite Review PDF
Ably, Mohammed Algebraic independence of some numbers with “good” diophantine approximation. (Indépendance algébrique de certains nombres admettant une “bonne” approximation diophantienne.) (French) Zbl 0758.11033 C. R. Acad. Sci., Paris, Sér. I 313, No. 10, 653-655 (1991). Reviewer: Michel Waldschmidt (Paris) MSC: 11J85 11J82 × Cite Format Result Cite Review PDF
Zheng, Hongliu Some application of Hermite-Mahler formulae. (Chinese. English summary) Zbl 0742.11037 J. Shandong Univ., Nat. Sci. Ed. 26, No. 2, 145-153 (1991). Reviewer: Xu Guangshan (Beijing) MSC: 11J82 11J72 × Cite Format Result Cite Review PDF
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 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Nishioka, Kumiko Algebraic independence measures of the values of Mahler functions. (English) Zbl 0736.11034 J. Reine Angew. Math. 420, 203-214 (1991). Reviewer: R.Wallisser (Freiburg i.Br.) MSC: 11J85 11J91 × Cite Format Result Cite Review PDF Full Text: DOI Crelle EuDML
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 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Shmelev, A. A. Simultaneous approximations of exponentials by elements of fields of transcendence degree 1. (English. Russian original) Zbl 0739.11028 Math. Notes 48, No. 6, 1258-1266 (1990); translation from Mat. Zametki 48, No. 6, 126-136 (1990). Reviewer: K.Väänänen (Oulu) MSC: 11J85 11J13 11J17 × Cite Format Result Cite Review PDF Full Text: DOI
Waldschmidt, Michel Indépendance algébrique de nombres de Liouville. (Algebraic independence of Liouville numbers). (French) Zbl 0729.11035 Fifty years of polynomials, Proc. Conf. in Honour of Alain Durand, Paris/Fr. 1988, Lect. Notes Math. 1415, 225-235 (1990). Reviewer: A.J.van der Poorten (North Ryde) MSC: 11J85 11J82 30B10 11-02 × Cite Format Result Cite Review PDF
Shestakova, N. V. Estimates for the measure of mutual transcendence of certain numbers. (English. Russian original) Zbl 0722.11037 Mosc. Univ. Math. Bull. 45, No. 6, 15-18 (1990); translation from Vestn. Mosk. Univ., Ser. I 1990, No. 6, 14-18 (1990). Reviewer: Xu Guangshan (Beijing) MSC: 11J82 11J85 × Cite Format Result Cite Review PDF
Gorelov, V. A. On estimation of measures of algebraic independence of values of E- functions. (Russian) Zbl 0717.11027 Sib. Mat. Zh. 31, No. 5(183), 31-45 (1990). Reviewer: Xu Guangshan MSC: 11J91 11J82 × Cite Format Result Cite Review PDF Full Text: EuDML
Waldschmidt, Michel; Zhu, Yaochen Algebraic independence of certain numbers related to Liouville numbers. (English) Zbl 0697.10029 Sci. China, Ser. A 33, No. 3, 257-268 (1990). Reviewer: P.Philippon MSC: 11J85 11J89 11J82 × Cite Format Result Cite Review PDF
Ably, Mohammed Mesure d’approximation simultanée. (Simultaneous approximation measures). (French) Zbl 0705.11035 Ann. Fac. Sci. Toulouse, V. Sér., Math. 10, No. 2, 259-289 (1989). Reviewer: D.W.Masser MSC: 11J82 × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML
Shidlovskii, A. B. [Brownawell, W. Dale] Transcendental numbers. With a foreword by W. Dale Brownawell. Transl. from the Russian by Neal Koblitz. (English) Zbl 0689.10043 De Gruyter Studies in Mathematics, 12. Berlin etc.: Walter de Gruyter. xix, 466 p. $ 77.00; DM 168.00, $ 89.00 (1989). Reviewer: Peter Bundschuh (Köln) MSC: 11J81 × Cite Format Result Cite Review PDF Backlinks: MO
Ably, Mohammed Mesure d’approximation simultanée. (Simultaneous approximation measure). (French) Zbl 0681.10023 C. R. Acad. Sci., Paris, Sér. I 307, No. 8, 371-374 (1988). Reviewer: F.Gramain MSC: 11J81 × Cite Format Result Cite Review PDF
Nesterenko, Yu. V. Effective estimates of the measure of algebraic independence of the values of E-functions. (English. Russian original) Zbl 0659.10042 Mosk. Univ. Math. Bull. 43, No. 1, 84-87 (1988); translation from Vestn. Mosk. Univ., Ser. I 1988, No. 4, 85-88 (1988). Reviewer: W.D.Brownawell MSC: 11J85 11J81 34A99 × Cite Format Result Cite Review PDF
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 × Cite Format Result Cite Review PDF
Chudnovsky, D. V.; Chudnovsky, G. V. Approximations and complex multiplication according to Ramanujan. (English) Zbl 0647.10002 Ramanujan revisited, Proc. Conf., Urbana-Champaign/Illinois 1987, 375-472 (1988). Reviewer: J.Wolfart MSC: 11-02 14-02 11J81 14K22 11-04 11Y60 11Y05 11J85 30F10 30B40 34M99 41A21 33C05 68W99 11A41 14-04 × Cite Format Result Cite Review PDF
Faisant, Alain; Philibert, Georges Quelques résultats de transcendance liés à l’invariant modulaire j. (Some transcendence results related to the modular invariant j). (French) Zbl 0633.10035 J. Number Theory 25, 184-200 (1987). Reviewer: E.Reyssat MSC: 11J81 11J85 11F03 × Cite Format Result Cite Review PDF Full Text: DOI
Sieburg, Hans-Bernd Transcendence theory over non-local fields. (English) Zbl 0632.10036 Analytic number theory and diophantine problems, Proc. Conf., Stillwater/Okla. 1984, Prog. Math. 70, 333-346 (1987). Reviewer: D.W.Masser MSC: 11J81 11J85 × Cite Format Result Cite Review PDF
Shidlovskiĭ, A. B. Transcendental numbers. (Трансцендентные числа.) (Russian) Zbl 0629.10026 Moskva: “Nauka”. Glavnaya Redaktsiya Fiziko-Matematicheskoĭ Literatury. 448 p. R. 4.60 (1987). Reviewer: Keijo Väänänen (Oulu) MSC: 11J81 11-02 11J85 11J91 × Cite Format Result Cite Review PDF
Brownawell, W. Dale; Tubbs, Robert Large transcendence degree revisited. II: The CM case. (English) Zbl 0626.10031 Diophantine approximation and transcendence theory, Semin., Bonn./FRG 1985, Lect. Notes Math. 1290, 175-188 (1987). Reviewer: Michel Waldschmidt (Paris) MSC: 11J81 14H52 14K22 × Cite Format Result Cite Review PDF
Brownawell, W. Dale Large transcendence degree revisited. I: Exponential and non-CM cases. (English) Zbl 0626.10030 Diophantine approximation and transcendence theory, Semin., Bonn/FRG 1985, Lect. Notes Math. 1290, 149-173 (1987). Reviewer: P.Philippon MSC: 11J81 11J85 13C99 × Cite Format Result Cite Review PDF
Diaz, Guy Grands degrés de transcendance pour des familles d’exponentielles. (Large transcendence degrees for exponential families). (French) Zbl 0621.10023 C. R. Acad. Sci., Paris, Sér. I 305, 159-162 (1987). Reviewer: P.Philippon MSC: 11J85 11J81 × Cite Format Result Cite Review PDF
Philippon, Patrice Indépendance et groupes algébriques. (Independence and algebraic groups). (French) Zbl 0619.10030 Number theory, Proc. Conf., Montreal/Can. 1985, CMS Conf. Proc. 7, 279-284 (1987). Reviewer: M.Waldschmidt MSC: 11J85 11J81 14L10 33E05 × Cite Format Result Cite Review PDF
Eckmann, Steffen Über die lineare Unabhängigkeit der Werte gewisser Reihen. (On the linear independence of values of certain series). (German) Zbl 0618.10034 Result. Math. 11, 8-43 (1987). Reviewer: M.Huttner MSC: 11J81 11J85 33C60 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF