Document Search Results

On $G$-functions and Padé approximations. (English) Zbl 1132.11335

Kanemitsu, Shigeru (ed.) et al., Number theoretic methods. Future trends. Proceedings of the 2nd China-Japan seminar, Iizuka, Fukuoka, Japan, March 12–16, 2001. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-1080-X/hbk). Dev. Math. 8, 301-310 (2002).

MSC: 11J91

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Bundschuh, Peter

New applications of a result of Galochkin on linear independence. (English) Zbl 1241.11080

Kanemitsu, Shigeru (ed.) et al., Number theoretic methods. Future trends. Proceedings of the 2nd China-Japan seminar, Iizuka, Fukuoka, Japan, March 12–16, 2001. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-1080-X/hbk). Dev. Math. 8, 55-66 (2002).

MSC: 11J72 11J91 33D15

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Amou, Masaaki; Matala-aho, Tapani

Arithmetical properties of solutions of linear second order $q$-difference equations. (English) Zbl 1132.11334

Kanemitsu, Shigeru (ed.) et al., Number theoretic methods. Future trends. Proceedings of the 2nd China-Japan seminar, Iizuka, Fukuoka, Japan, March 12–16, 2001. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-1080-X/hbk). Dev. Math. 8, 15-29 (2002).

MSC: 11J82 11J70 39A13

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Amou, Masaaki

Linear independence of the values of $q$-hypergeometric series. (Japanese) Zbl 1127.11330

RIMS Kokyuroku 1274, 177-182 (2002).

MSC: 11J72 11J91 33D15

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Nagata, Makoto

On Diophantine approximations related to $G$-functions. (Japanese) Zbl 1127.11332

RIMS Kokyuroku 1274, 94-99 (2002).

MSC: 11J91

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Kanoko, Tomoaki

Transcendence of certain reciprocal sums of linear recurrences. (Japanese) Zbl 1127.11331

RIMS Kokyuroku 1274, 115-122 (2002).

MSC: 11J81 11J72

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Özdemir, Ahmet S.

On the measure of transcendence of $\gamma=\displaystyle\sum_{k=0}^{\infty} G^{-s^k}_k$ formal Laurent series. (English) Zbl 1155.11335

Bull. Pure Appl. Sci., Sect. E, Math. Stat. 21, No. 1, 173-184 (2002).

MSC: 11J82

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Richardson, Daniel; Langley, Simon

Some observations on familiar numbers. (English) Zbl 1072.68131

Mora, Teo (ed.), ISSAC 2002. Proceedings of the 2002 international symposium on symbolic and algebraic computation, Lille, France, July 07–10, 2002. New York, NY: ACM Press (ISBN 1-58113-484-3/pbk). 214-220 (2002).

MSC: 68W30 65G99 11J82

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Zudilin, V. V.

Very well-poised hypergeometric series and multiple integrals. (English. Russian original) Zbl 1229.33011

Russ. Math. Surv. 57, No. 4, 824-826 (2002); translation from Usp. Mat. Nauk 57, No. 4, 177-178 (2002).

MSC: 33C20 33C60 11J82 11J91

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Sorokin, V. N.

Cyclic graphs and Apéry’s theorem. (English. Russian original) Zbl 1047.11070

Russ. Math. Surv. 57, No. 3, 535-571 (2002); translation from Usp. Mat. Nauk 57, No. 3, 99-134 (2002).

Reviewer: Jacek Gilewicz (Marseille)

MSC: 11J72 41A21 11J82

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Zudilin, W. V.

On the irrationality measure for a $q$-analogue of $\zeta(2)$. (English. Russian original) Zbl 1044.11067

Sb. Math. 193, No. 8, 1151-1172 (2002); translation from Mat. Sb. 193, No. 8, 49-70 (2002).

Reviewer: Tanguy Rivoal (Caen)

MSC: 11J82 11J72 11J91

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Tijdeman, R.

Some applications of Diophantine approximation. (English) Zbl 1045.11022

Bennett, M. A. (ed.) et al., Number theory for the millennium III. Proceedings of the millennial conference on number theory, Urbana-Champaign, IL, USA, May 21–26, 2000. Natick, MA: A K Peters (ISBN 1-56881-152-7/hbk). 261-284 (2002).

Reviewer: Jan-Hendrik Evertse (Leiden)

MSC: 11D61 11J81 11J68 11J86

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Bombieri, Enrico

Forty years of effective results in Diophantine theory. (English) Zbl 1080.11053

Wüstholz, Gisbert (ed.), A panorama in number theory or The view from Baker’s garden. Based on a conference in honor of Alan Baker’s 60th birthday, Zürich, Switzerland, 1999. Cambridge: Cambridge University Press (ISBN 0-521-80799-9/hbk), 194-213 (2002).

Reviewer: Maurice Mignotte (Strasbourg)

MSC: 11J68 11J81 11J86 11D59 11-02

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Nesterenko, Yu. V.

On the algebraic independence of numbers. (English) Zbl 1044.11071

Wüstholz, Gisbert (ed.), A panorama in number theory or The view from Baker’s garden. Based on a conference in honor of Alan Baker’s 60th birthday, Zürich, Switzerland, 1999. Cambridge: Cambridge University Press (ISBN 0-521-80799-9/hbk). 148-167 (2002).

Reviewer: P. Philippon (Paris)

MSC: 11J91 11J85 11-02

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Cohen, Paula B.; Wüstholz, Gisbert

Application of the André-Oort conjecture to some questions in transcendence. (English) Zbl 1051.11039

Wüstholz, Gisbert (ed.), A panorama in number theory or The view from Baker’s garden. Based on a conference in honor of Alan Baker’s 60th birthday, Zürich, Switzerland, 1999. Cambridge: Cambridge University Press (ISBN 0-521-80799-9/hbk). 89-106 (2002).

Reviewer: Zhu Yaochen (Beijing)

MSC: 11J91 11J81

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Chambert-Loir, Antoine

Algebraicity theorems in Diophantine geometry following J.-B. Bost, Y. André, D. & G. Chudnovsky. (Théorèmes d’algébricité en géométrie diophantienne d’après J.-B. Bost, Y. André, D. & G. Chudnovsky.) (French) Zbl 1044.11055

Bourbaki seminar. Volume 2000/2001. Exposés 880-893. Paris: Société Mathématique de France (ISBN 2-85629-130-9/pbk). Astérisque 282, 175-209, Exp. No. 886 (2002).

Reviewer: Paul Vojta (Berkeley)

MSC: 11G35 11J81 14G40

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Full Text: Numdam EuDML

Adhikari, Sukumar Das

Transcendental infinite sums and some related questions. (English) Zbl 1032.11030

Agarwal, A. K. (ed.) et al., Number theory and discrete mathematics. Proceedings of the international conference in honour of Srinivasa Ramanujan, Chandigarh, India, October 2-6, 2000. Basel: Birkhäuser. Trends in Mathematics. 169-178 (2002).

Reviewer: J.Hančl (Ostrava)

MSC: 11J81

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Waldschmidt, M.

Multiple polylogarithms: an introduction. (English) Zbl 1035.11033

Agarwal, A. K. (ed.) et al., Number theory and discrete mathematics. Proceedings of the international conference in honour of Srinivasa Ramanujan, Chandigarh, India, October 2–6, 2000. Basel: Birkhäuser (ISBN 3-7643-6720-2/hbk). Trends in Mathematics, 1-12 (2002).

Reviewer: Damien Roy (Ottawa)

MSC: 11J91 11G55 11M41 33B30

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Yu, Xiuyuan

On the algebraic approximation measure of a class of functions. (Chinese. English summary) Zbl 1086.11038

J. Math., Wuhan Univ. 22, No. 3, 292-296 (2002).

Reviewer: Zhu Yaochen (Beijing)

MSC: 11J81

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Zudilin, V. V.

Diophantine problems for $q$-zeta values. (English. Russian original) Zbl 1044.11066

Math. Notes 72, No. 6, 858-862 (2002); translation from Mat. Zametki 72, No. 6, 936-940 (2002).

Reviewer: Tanguy Rivoal (Caen)

MSC: 11J82 11J72

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Zudilin, V. V.

On the integrality of power expansions related to hypergeometric series. (English. Russian original) Zbl 1043.11060

Math. Notes 71, No. 5, 604-616 (2002); translation from Mat. Zametki 71, No. 5, 662-676 (2002).

Reviewer: Tanguy Rivoal (Caen)

MSC: 11J91 14J32

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Ivankov, P. L.

On simultaneous approximations that take into account the specifics of the homogeneous case. (English. Russian original) Zbl 1026.11062

Math. Notes 71, No. 3, 355-361 (2002); translation from Mat. Zametki 71, No. 3, 390-397 (2002).

Reviewer: Zhu Yaochen (Beijing)

MSC: 11J82 11J91

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Wakabayashi, Isao

Cubic Thue inequalities with negative discriminant. (English) Zbl 1042.11021

J. Number Theory 97, No. 2, 222-251 (2002).

Reviewer: Günter Lettl (Graz)

MSC: 11D59 11J82 11D75

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Bertolin, Cristiana

Periods of 1-motives and transcendence. (Périodes de 1-motifs et transcendance.) (French) Zbl 1067.11041

J. Number Theory 97, No. 2, 204-221 (2002).

Reviewer: Michel Waldschmidt (Paris)

MSC: 11J95 11G05 11J81

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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

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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

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Zhu, Yaochen

Transcendence of certain trigonometric series. (English) Zbl 1031.11044

Acta Math. Sin., Engl. Ser. 18, No. 3, 481-488 (2002).

MSC: 11J72 11J91

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David, Sinnou; Philippon, Patrice

Minorations des hauteurs normalisées des sous-variétés de variétés abeliennes. II. (Lower bounds for normalized heights of subvarieties of Abelian varieties. II.). (French) Zbl 1030.11026

Comment. Math. Helv. 77, No. 4, 639-700 (2002).

Reviewer: Michel Waldschmidt (Paris)

MSC: 11G10 14G40 11J81

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Zhu, Yaochen

Algebraic independence of values of certain trigonometric series. (Chinese. English summary) Zbl 1113.11301

Acta Math. Sin. 45, No. 6, 1079-1086 (2002).

MSC: 11J85 11J91

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Harman, Glyn

Nonlinear Diophantine approximation of complex numbers. (English) Zbl 1062.11050

Math. Proc. Camb. Philos. Soc. 133, No. 2, 205-212 (2002).

Reviewer: M. M. Dodson (Heslington)

MSC: 11J83 11J81 11J25 11J71

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Cohen, Paula B.; van der Poorten, Alfred J.

Ideal constructions and irrationality measures of roots of algebraic numbers. (English) Zbl 1040.11052

Ill. J. Math. 46, No. 1, 63-80 (2002).

Reviewer: Maurice Mignotte (Strasbourg)

MSC: 11J68 11J82

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Duverney, Daniel; Kanoko, Tomoaki; Tanaka, Taka-aki

Transcendence of certain reciprocal sums of linear recurrences. (English) Zbl 1012.11062

Monatsh. Math. 137, No. 2, 115-128 (2002).

Reviewer: Peter Bundschuh (Köln)

MSC: 11J81 11B37

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Zilber, Boris

A theory of a generic function with derivations. (English) Zbl 1013.03043

Zhang, Yi (ed.), Logic and algebra. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 302, 85-99 (2002).

MSC: 03C60 12L12 03C65 11J81 11U09

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Chatham, R. Douglas; Dobbs, David E.

On pseudo-valuation domains whose overrings are going-down domains. (English) Zbl 1059.13004

Houston J. Math. 28, No. 1, 13-19 (2002).

Reviewer: M. E. Keating (London)

MSC: 13B24 13G05 12F20

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Fogg, N. Pytheas (ed.); Berthé, Valérie (ed.); Ferenczi, Sébastien (ed.); Mauduit, Christian (ed.); Siegel, A. (ed.)

Substitutions in dynamics, arithmetics and combinatorics. (English) Zbl 1014.11015

Lecture Notes in Mathematics. 1794. Berlin: Springer. xv, 402 p. EUR 57.95/net; sFr. 96.50; £40.50; $ 76.80 (2002).

Reviewer: Jean-Paul Allouche (Orsay)

MSC: 11B85 11-02 37-02 05-02 68Q45 68R15 11A55 11A63 11J70 37B10 28D99 37A45 05A17

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Backlinks: MO MO

Amou, Masaaki; Katsurada, Masanori; Väänänen, Keijo

On the values of certain $q$-hypergeometric series. II. (English) Zbl 1027.11048

Jia, Chaohua (ed.) et al., Analytic number theory. Proceedings of the 1st China-Japan seminar on number theory, Beijing, China, September 13-17, 1999 and the annual conference on analytic number theory, Kyoto, Japan, November 29-December 3, 1999. Dordrecht: Kluwer Academic Publishers. Dev. Math. 6, 17-25 (2002).

Reviewer: Peter Bundschuh (Köln)

MSC: 11J72 11J82

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Roy, Damien

Interpolation formulas and auxiliary functions. (English) Zbl 1010.11039

J. Number Theory 94, No. 2, 248-285 (2002).

Reviewer: P.Philippon (Paris)

MSC: 11J81 11J85 11J89 41A05 32E30

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Bundschuh, Peter

Introduction to number theory. 5., überarbeitete und aktualisierte Aufl. (Einführung in die Zahlentheorie.) (German) Zbl 1054.11002

Springer-Lehrbuch. Berlin: Springer (ISBN 3-540-43579-4/pbk). xiv, 336 S. (2002).

Reviewer: Olaf Ninnemann (Berlin)

MSC: 11-01 11Axx 11N05 11M06 11J81 11Dxx

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Gouillon, Nicolas

A zero lemma. (Un lemme de zéros.) (French) Zbl 1031.11046

C. R., Math., Acad. Sci. Paris 335, No. 2, 167-170 (2002).

Reviewer: Michel Waldschmidt (Paris)

MSC: 11J95 11J81 32A60 14A05 14C17 14L10 33B10 11J86

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Gutierrez, Jaime; Rubio, Rosario; Sevilla, David

On multivariate rational function decomposition. (English) Zbl 1043.12006

J. Symb. Comput. 33, No. 5, 545-562 (2002).

Reviewer: Yueh-er Kuo (Knoxville)

MSC: 12Y05 13P99 12F20

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Zudilin, Wadim

Remarks on irrationality of $q$-harmonic series. (English) Zbl 1044.11068

Manuscr. Math. 107, No. 4, 463-477 (2002).

Reviewer: Tanguy Rivoal (Caen)

MSC: 11J82 33D15

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Nishioka, Kumiko

Algebraic independence of reciprocal sums of binary recurrences. II. (English) Zbl 1020.11050

Monatsh. Math. 136, No. 2, 123-141 (2002).

Reviewer: Peter Bundschuh (Köln)

MSC: 11J85 11J81 11J91

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Full Text: DOI EuDML

Bruiltet, Sylvain

From a simultaneous approximation measure to an irrationality measure: the cases ${\varGamma}(1/4)$ and ${\varGamma}(1/3)$. (D’une mesure d’approximation simultanée à une mesure d’irrationalité : le cas de ${\varGamma}(1/4)$ et ${\varGamma}(1/3)$.) (French) Zbl 1069.11029

Acta Arith. 104, No. 3, 243-281 (2002).

Reviewer: Michel Waldschmidt (Paris)

MSC: 11J82 11J89 11J91

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Bauer, Mark; Bennett, Michael A.

Applications of the hypergeometric method to the generalized Ramanujan-Nagell equation. (English) Zbl 1010.11020

Ramanujan J. 6, No. 2, 209-270 (2002).

Reviewer: Nikos Tzanakis (Iraklion)

MSC: 11D61 11D45 11J82

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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

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Yao, Jia-Yan

Some transcendental functions over function fields with positive characteristic. (English. Abridged French version) Zbl 1074.11038

C. R., Math., Acad. Sci. Paris 334, No. 11, 939-943 (2002).

MSC: 11J81 11B85 11J91

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Brownawell, W. Dale; Papanikolas, Matthew A.

Linear independence of $\Gamma$ values in positive characteristic. (English) Zbl 1002.11051

J. Reine Angew. Math. 549, 91-148 (2002).

Reviewer: Michel Waldschmidt (Paris)

MSC: 11G09 11J93

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Corvaja, Pietro; Zannier, Umberto

Some new applications of the subspace theorem. (English) Zbl 1010.11038

Compos. Math. 131, No. 3, 319-340 (2002).

Reviewer: Jan-Hendrik Evertse (Leiden)

MSC: 11J81 11J25 11D61

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Surroca, Andrea

On the number of algebraic points where an analytic transcendental function takes algebraic values. (Sur le nombre de points algébriques où une fonction analytique transcendante prend des valeurs algébriques.) (French. Abridged English version) Zbl 1013.11037

C. R., Math., Acad. Sci. Paris 334, No. 9, 721-725 (2002).

Reviewer: F.Gramain (Saint-Etienne)

MSC: 11J81 30D10 11J99

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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

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Bouscaren, E.; Delon, F.

Minimal groups in separably closed fields. (English) Zbl 1002.03028

J. Symb. Log. 67, No. 1, 239-259 (2002).

MSC: 03C60 03C45 12L12

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Fischler, Stéphane

Formes linéaires en polyzêtas et intégrales multiples. arXiv:math/0202064

Preprint, arXiv:math/0202064 [math.NT] (2002).

MSC: 11J82 11J72

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Full Text: arXiv

Zudilin, Wadim

Multiple-integral representations of very-well-poised hypergeometric series. arXiv:math/0206177

Preprint, arXiv:math/0206177 [math.CA] (2002).

MSC: 33C20 33C60 11J82

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Full Text: arXiv

Found 53 Documents (Results 1–53)

On \(G\)-functions and Padé approximations. (English) Zbl 1132.11335

New applications of a result of Galochkin on linear independence. (English) Zbl 1241.11080

Arithmetical properties of solutions of linear second order \(q\)-difference equations. (English) Zbl 1132.11334

Linear independence of the values of \(q\)-hypergeometric series. (Japanese) Zbl 1127.11330

On Diophantine approximations related to \(G\)-functions. (Japanese) Zbl 1127.11332

Transcendence of certain reciprocal sums of linear recurrences. (Japanese) Zbl 1127.11331

On the measure of transcendence of \(\gamma=\displaystyle\sum_{k=0}^{\infty} G^{-s^k}_k\) formal Laurent series. (English) Zbl 1155.11335

Some observations on familiar numbers. (English) Zbl 1072.68131

Very well-poised hypergeometric series and multiple integrals. (English. Russian original) Zbl 1229.33011

Cyclic graphs and Apéry’s theorem. (English. Russian original) Zbl 1047.11070

On the irrationality measure for a \(q\)-analogue of \(\zeta(2)\). (English. Russian original) Zbl 1044.11067

Some applications of Diophantine approximation. (English) Zbl 1045.11022

Forty years of effective results in Diophantine theory. (English) Zbl 1080.11053

On the algebraic independence of numbers. (English) Zbl 1044.11071

Application of the André-Oort conjecture to some questions in transcendence. (English) Zbl 1051.11039

Algebraicity theorems in Diophantine geometry following J.-B. Bost, Y. André, D. & G. Chudnovsky. (Théorèmes d’algébricité en géométrie diophantienne d’après J.-B. Bost, Y. André, D. & G. Chudnovsky.) (French) Zbl 1044.11055

Transcendental infinite sums and some related questions. (English) Zbl 1032.11030

Multiple polylogarithms: an introduction. (English) Zbl 1035.11033

On the algebraic approximation measure of a class of functions. (Chinese. English summary) Zbl 1086.11038

Diophantine problems for \(q\)-zeta values. (English. Russian original) Zbl 1044.11066

On the integrality of power expansions related to hypergeometric series. (English. Russian original) Zbl 1043.11060

On simultaneous approximations that take into account the specifics of the homogeneous case. (English. Russian original) Zbl 1026.11062

Cubic Thue inequalities with negative discriminant. (English) Zbl 1042.11021

Periods of 1-motives and transcendence. (Périodes de 1-motifs et transcendance.) (French) Zbl 1067.11041

Irrationality measures for the series of reciprocals from recurrence sequences. (English) Zbl 1069.11030

Arithmetic properties of solutions of certain functional equations in several variables. (English) Zbl 1025.11024

Transcendence of certain trigonometric series. (English) Zbl 1031.11044

Minorations des hauteurs normalisées des sous-variétés de variétés abeliennes. II. (Lower bounds for normalized heights of subvarieties of Abelian varieties. II.). (French) Zbl 1030.11026

Algebraic independence of values of certain trigonometric series. (Chinese. English summary) Zbl 1113.11301

Nonlinear Diophantine approximation of complex numbers. (English) Zbl 1062.11050

Ideal constructions and irrationality measures of roots of algebraic numbers. (English) Zbl 1040.11052

Transcendence of certain reciprocal sums of linear recurrences. (English) Zbl 1012.11062

A theory of a generic function with derivations. (English) Zbl 1013.03043

On pseudo-valuation domains whose overrings are going-down domains. (English) Zbl 1059.13004

Substitutions in dynamics, arithmetics and combinatorics. (English) Zbl 1014.11015

On the values of certain \(q\)-hypergeometric series. II. (English) Zbl 1027.11048

Interpolation formulas and auxiliary functions. (English) Zbl 1010.11039

Introduction to number theory. 5., überarbeitete und aktualisierte Aufl. (Einführung in die Zahlentheorie.) (German) Zbl 1054.11002

A zero lemma. (Un lemme de zéros.) (French) Zbl 1031.11046

On multivariate rational function decomposition. (English) Zbl 1043.12006

Remarks on irrationality of \(q\)-harmonic series. (English) Zbl 1044.11068

Algebraic independence of reciprocal sums of binary recurrences. II. (English) Zbl 1020.11050

From a simultaneous approximation measure to an irrationality measure: the cases \({\varGamma}(1/4)\) and \({\varGamma}(1/3)\). (D’une mesure d’approximation simultanée à une mesure d’irrationalité : le cas de \({\varGamma}(1/4)\) et \({\varGamma}(1/3)\).) (French) Zbl 1069.11029

Applications of the hypergeometric method to the generalized Ramanujan-Nagell equation. (English) Zbl 1010.11020

Measures of simultaneous approximation for quasi-periods of Abelian varieties. (English) Zbl 1030.11033

Some transcendental functions over function fields with positive characteristic. (English. Abridged French version) Zbl 1074.11038

Linear independence of \(\Gamma\) values in positive characteristic. (English) Zbl 1002.11051

Some new applications of the subspace theorem. (English) Zbl 1010.11038

On the number of algebraic points where an analytic transcendental function takes algebraic values. (Sur le nombre de points algébriques où une fonction analytique transcendante prend des valeurs algébriques.) (French. Abridged English version) Zbl 1013.11037

Transcendence of the values of certain series with Hadamard’s gaps. (English) Zbl 0998.11037

Minimal groups in separably closed fields. (English) Zbl 1002.03028

Formes linéaires en polyzêtas et intégrales multiples. arXiv:math/0202064

Multiple-integral representations of very-well-poised hypergeometric series. arXiv:math/0206177

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