Adamczewski, Boris; Faverjon, Colin Algebraic relations between values of Siegel \(E\)-functions and Mahler \(M\)-functions. (Relations algébriques entre valeurs de \(E\)-fonctions ou de \(M\)-fonctions.) (French. English summary) Zbl 07939454 C. R., Math., Acad. Sci. Paris 362, 1215-1241 (2024). Reviewer: Michel Waldschmidt (Paris) MSC: 11J81 11J91 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Fischler, S.; Rivoal, T. Relations between values of arithmetic Gevrey series, and applications to values of the gamma function. (English) Zbl 07841165 J. Number Theory 261, 36-54 (2024). MSC: 11J91 33B15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv HAL
Bostan, Alin; Rivoal, Tanguy; Salvy, Bruno Minimization of differential equations and algebraic values of \(E\)-functions. (English) Zbl 07810339 Math. Comput. 93, No. 347, 1427-1472 (2024). MSC: 68W30 11J81 16S32 34M15 33F10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Adamczewski, Boris; Faverjon, Colin A new proof of Nishioka’s theorem in Mahler’s method. (English) Zbl 1536.11115 C. R., Math., Acad. Sci. Paris 361, 1011-1028 (2023). Reviewer: Jaroslav Hančl (Ostrava) MSC: 11J81 11J85 12H05 11J91 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Adamczewski, Boris; Bell, Jason; Smertnig, Daniel A height gap theorem for coefficients of Mahler functions. (English) Zbl 1531.11067 J. Eur. Math. Soc. (JEMS) 25, No. 7, 2525-2571 (2023). Reviewer: Tanguy Rivoal (Grenoble) MSC: 11J81 39A06 11B85 11G50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Rivoal, Tanguy Factors of \(E\)-operators with an \(\eta\)-apparent singularity at zero. (English) Zbl 1503.11105 J. Math. Soc. Japan 74, No. 3, 719-733 (2022). Reviewer: Michel Waldschmidt (Paris) MSC: 11J91 33E30 34M05 × Cite Format Result Cite Review PDF Full Text: DOI HAL
Lepetit, G. Quantitative problems on the size of \(G\)-operators. (English) Zbl 1496.13039 Manuscr. Math. 169, No. 1-2, 51-75 (2022). Reviewer: Vladimir P. Kostov (Nice) MSC: 13N10 34M03 34M05 11J72 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Rivoal, Tanguy On Galochkin’s characterization of hypergeometric \(G\)-functions. (English) Zbl 1505.33005 Mosc. J. Comb. Number Theory 11, No. 1, 11-19 (2022). Reviewer: Showkat Ahmad (Sopore) MSC: 33C20 11J91 34M15 × Cite Format Result Cite Review PDF Full Text: DOI HAL
Hirata-Kohno, Noriko Diophantine approximation. (English. Japanese original) Zbl 1489.11102 Sugaku Expo. 34, No. 2, 205-229 (2021); translation from Sūgaku 64, No. 3, 254-277 (2012). Reviewer: Clemens Fuchs (Salzburg) MSC: 11J68 11J87 11J72 11J86 11-02 11J89 × Cite Format Result Cite Review PDF Full Text: DOI
Fresán, Javier; Jossen, Peter A non-hypergeometric \(E\)-function. (English) Zbl 1482.11099 Ann. Math. (2) 194, No. 3, 903-942 (2021). Reviewer: Tanguy Rivoal (Grenoble) MSC: 11J91 33C20 34M35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ferguson, Timothy Algebraic properties of Э-functions. (English) Zbl 1489.11106 J. Number Theory 229, 168-178 (2021). Reviewer: Tanguy Rivoal (Grenoble) MSC: 11J91 34G10 33F10 × Cite Format Result Cite Review PDF Full Text: DOI
Adamczewski, Boris; Faverjon, Colin Mahler method: linear relations, transcendence and applications to automatic numbers. (Méthode de Mahler: relations linéaires, transcendance et applications aux nombres automatiques.) (French. English summary) Zbl 1440.11132 Proc. Lond. Math. Soc. (3) 115, No. 1, 55-90 (2017). MSC: 11J81 11J85 11B85 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link HAL
Rivoal, Tanguy; Roques, Julien Holomorphic solutions of \(E\)-operators. (English) Zbl 1430.11103 Isr. J. Math. 220, No. 1, 275-282 (2017). MSC: 11J91 30B10 33E30 × Cite Format Result Cite Review PDF Full Text: DOI
Rivoal, T.; Roques, J. On the algebraic dependence of \(E\)-functions. (English) Zbl 1398.30016 Bull. Lond. Math. Soc. 48, No. 2, 271-279 (2016). MSC: 30D15 11J91 34M35 × Cite Format Result Cite Review PDF Full Text: DOI
Kühne, Lars Logarithms of algebraic numbers. (English. French summary) Zbl 1387.11055 J. Théor. Nombres Bordx. 27, No. 2, 499-535 (2015). MSC: 11J81 11J82 × Cite Format Result Cite Review PDF Full Text: DOI
Dreyfus, Thomas Confluence of meromorphic solutions of \(q\)-difference equations. (Confluence de solutions méromorphes d’équations aux \(q\)-différences.) (English. French summary) Zbl 1331.39006 Ann. Inst. Fourier 65, No. 2, 431-507 (2015). Reviewer: Miloš Čanak (Beograd) MSC: 39A13 34M40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
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
Lagarias, Jeffrey C. Euler’s constant: Euler’s work and modern developments. (English) Zbl 1282.11002 Bull. Am. Math. Soc., New Ser. 50, No. 4, 527-628 (2013). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11-02 11-03 01A50 11Y60 11J72 11J81 11M06 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Si, Jianguo; Zhao, Houyu Small divisor problem in dynamical systems and analytic solutions of a \(q\)-difference equation with a singularity at the origin. (English) Zbl 1210.39005 Result. Math. 58, No. 3-4, 337-353 (2010). Reviewer: Roman Šimon Hilscher (Brno) MSC: 39A13 × Cite Format Result Cite Review PDF Full Text: DOI
Matala-Aho, Tapani On \(q\)-analogues of divergent and exponential series. (English) Zbl 1169.11031 J. Math. Soc. Japan 61, No. 1, 291-313 (2009). Reviewer: Jaroslav Hančl (Ostrava) MSC: 11J82 11J72 33D15 × Cite Format Result Cite Review PDF Full Text: DOI
Chirskii, V. G. Siegel-Shidlovskii method in \(p\)-adic domain. (English. Russian original) Zbl 1204.11125 J. Math. Sci., New York 146, No. 2, 5791-5797 (2007); translation from Fundam. Prikl. Mat. 11, No. 6, 221-230 (2005). MSC: 11J91 11-02 × Cite Format Result Cite Review PDF Full Text: DOI
Manjra, Said; Remmal, Salah-eddine \(p\)-adic differential equations and arithmetic Gevrey series. (Equations différentielles \(p\)-adiques et séries Gevrey arithmétiques.) (English) Zbl 1207.12005 Math. Ann. 334, No. 1, 37-64 (2006). Reviewer: Olaf Ninnemann (Berlin) MSC: 12H25 34A25 34M15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Amou, Masaaki; Väänänen, Keijo Linear independence of the values of \(q\)-hypergeometric series and related functions. (English) Zbl 1095.11038 Ramanujan J. 9, No. 3, 317-339 (2005). Reviewer: Peter Bundschuh (Köln) MSC: 11J72 × Cite Format Result Cite Review PDF Full Text: DOI
Bertrand, Daniel; Chirskii, Vladimir; Yebbou, Johan Effective estimates for global relations on Euler-type series. (English) Zbl 1176.11036 Ann. Fac. Sci. Toulouse, Math. (6) 13, No. 2, 241-260 (2004). MSC: 11J91 11J61 11J72 11J85 34M15 34M35 × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML Link
André, Yves Arithmetic Gevrey series and transcendence. A survey. (English) Zbl 1136.11315 J. Théor. Nombres Bordx. 15, No. 1, 1-10 (2003). MSC: 11J81 × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML
Amou, Masaaki; Väänänen, Keijo Arithmetic properties of solutions of certain functional equations in several variables. (English) Zbl 1025.11024 J. Number Theory 96, No. 1, 89-104 (2002). Reviewer: R.Wallisser (Freiburg i.Br.) MSC: 11J72 11J82 × Cite Format Result Cite Review PDF Full Text: DOI