Diaz, Guy Products and quotients of linear forms of logarithms of algebraic numbers: conjectures and partial results. (Produits et quotients de combinaisons linéaires de logarithmes de nombres algébriques: conjectures et résultats partiels.) (French. English summary) Zbl 1163.11055 J. Théor. Nombres Bordx. 19, No. 2, 373-391 (2007). Reviewer: Michel Waldschmidt (Paris) MSC: 11J81 11J86 PDFBibTeX XMLCite \textit{G. Diaz}, J. Théor. Nombres Bordx. 19, No. 2, 373--391 (2007; Zbl 1163.11055) Full Text: DOI EuDML
Diaz, Guy Use of complex conjugation in the transcendence of values of the usual exponential function. (Utilisation de la conjugaison complexe dans l’étude de la transcendance de valeurs de la fonctions exponentielle usuelle.) (French) Zbl 1071.11046 J. Théor. Nombres Bordx. 16, No. 3, 535-553 (2004). Reviewer: Michel Waldschmidt (Paris) MSC: 11J81 11J91 PDFBibTeX XMLCite \textit{G. Diaz}, J. Théor. Nombres Bordx. 16, No. 3, 535--553 (2004; Zbl 1071.11046) Full Text: DOI Numdam EuDML
Nesterenko, Yu. V. (ed.); Philippon, Patrice (ed.) [Amoroso, Francesco; Bertrand, Daniel; Brownawell, W. Dale; Diaz, Guy; Laurent, Michel; Nishioka, Ku.; Rémond, Guy; Roy, Damien; Waldschmidt, Michel] Introduction to algebraic independence theory. With contributions from F. Amoroso, D. Bertrand, W. D. Brownawell, G. Diaz, M. Laurent, Yu. V. Nesterenko, K. Nishioka, P. Philippon, G. Rémond, D. Roy, M. Waldschmidt. (English) Zbl 0966.11032 Lecture Notes in Mathematics. 1752. Berlin: Springer. xiii, 256 p. (2001). Reviewer: François Gramain (Saint-Etienne) MSC: 11J85 11-02 11F03 11J91 PDFBibTeX XMLCite \textit{Yu. V. Nesterenko} (ed.) and \textit{P. Philippon} (ed.), Introduction to algebraic independence theory. With contributions from F. Amoroso, D. Bertrand, W. D. Brownawell, G. Diaz, M. Laurent, Yu. V. Nesterenko, K. Nishioka, P. Philippon, G. Rémond, D. Roy, M. Waldschmidt. Berlin: Springer (2001; Zbl 0966.11032) Full Text: DOI Link
Diaz, Guy Transcendence and algebraic independence: links between the elliptic and modular points of view. (Transcendance et indépendance algébrique: liens entre les points de vue elliptique et modulaire.) (French) Zbl 1115.11312 Ramanujan J. 4, No. 2, 157-199 (2000). MSC: 11J89 11J85 11J91 11F03 11F11 33E05 PDFBibTeX XMLCite \textit{G. Diaz}, Ramanujan J. 4, No. 2, 157--199 (2000; Zbl 1115.11312) Full Text: DOI
Diaz, Guy The four exponentials conjecture and D. Bertrand’s conjecture on the modular function. (La conjecture des quatre exponentielles et les conjectures de D. Bertrand sur la fonction modulaire.) (French) Zbl 0887.11030 J. Théor. Nombres Bordx. 9, No. 1, 229-245 (1997). Reviewer: Michel Waldschmidt (Paris) MSC: 11J81 11J91 11F03 PDFBibTeX XMLCite \textit{G. Diaz}, J. Théor. Nombres Bordx. 9, No. 1, 229--245 (1997; Zbl 0887.11030) Full Text: DOI Numdam EuDML EMIS
Barré-Sirieix, Katia; Diaz, Guy; Gramain, François; Philibert, Georges A proof of the Mahler-Manin conjecture. (Une preuve de la conjecture de Mahler-Manin.) (French) Zbl 0853.11059 Invent. Math. 124, No. 1-3, 1-9 (1996). Reviewer: V.Berthé (Marseille) MSC: 11J91 11G40 PDFBibTeX XMLCite \textit{K. Barré-Sirieix} et al., Invent. Math. 124, No. 1--3, 1--9 (1996; Zbl 0853.11059) Full Text: DOI
Diaz, Guy The Mahler-Manin conjecture. (La conjecture de Mahler-Manin.) (French) Zbl 0883.11037 Sémin. Anal., Univ. Blaise Pascal, Clermont II 10, Année 1994-1995, Exp. No. 24, 7 p. (1995). MSC: 11J89 11F03 11G40 PDFBibTeX XMLCite \textit{G. Diaz}, Sémin. Anal., Univ. Blaise Pascal, Clermont II 10, Exp. No. 24, 7\,p. (1995; Zbl 0883.11037)
Diaz, Guy Non homogeneous linear forms with one elliptic logarithm. (Minorations de combinaisons linéaires non homogènes pour un logarithme elliptique.) (French. Abridged English version) Zbl 0809.11037 C. R. Acad. Sci., Paris, Sér. I 318, No. 10, 879-883 (1994). Reviewer: D.Roy (Ottawa) MSC: 11J82 11J20 11J89 PDFBibTeX XMLCite \textit{G. Diaz}, C. R. Acad. Sci., Paris, Sér. I 318, No. 10, 879--883 (1994; Zbl 0809.11037)
Diaz, G. Une nouvelle mesure d’indépendance algébrique pour \((\alpha ^{\beta},\alpha ^{\beta ^ 2})\). (A new measure of algebraic independence for \((\alpha ^{\beta},\alpha ^{\beta ^ 2})\)). (French) Zbl 0659.10040 Acta Arith. 56, No. 1, 25-32 (1990). Reviewer: G.Diaz MSC: 11J85 11J81 PDFBibTeX XMLCite \textit{G. Diaz}, Acta Arith. 56, No. 1, 25--32 (1990; Zbl 0659.10040) Full Text: DOI EuDML
Diaz, Guy Généralisation d’un résultat de W. D. Brownawell - M. Waldschmidt. (Generalization of a result of W. D. Brownawell - M. Waldschmidt). (French) Zbl 0698.10022 Bull. Soc. Math. Fr. 117, No. 3, 267-283 (1989). Reviewer: P.Philippon MSC: 11J81 11J85 PDFBibTeX XMLCite \textit{G. Diaz}, Bull. Soc. Math. Fr. 117, No. 3, 267--283 (1989; Zbl 0698.10022) Full Text: DOI Numdam EuDML
Diaz, Guy Grands degrés de transcendance pour des familles d’exponentielles. (Large transcendence degrees for families of exponentials). (French) Zbl 0661.10047 J. Number Theory 31, No. 1, 1-23 (1989). Reviewer: A.Escassut MSC: 11J81 11J85 PDFBibTeX XMLCite \textit{G. Diaz}, J. Number Theory 31, No. 1, 1--23 (1989; Zbl 0661.10047) Full Text: DOI
Diaz, G. Mesure d’indépendance algébrique de \(\alpha ^{\beta}\), \(\alpha ^{\beta ^ 2}\). (Measure of algebraic independence of \(\alpha ^{\beta},\alpha ^{\beta ^ 2})\). (French) Zbl 0661.10048 Sémin. Théor. Nombres, Paris 1986-87, Prog. Math. 75, 129-135 (1988). Reviewer: A.Escassut MSC: 11J81 PDFBibTeX XML
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 PDFBibTeX XMLCite \textit{G. Diaz}, C. R. Acad. Sci., Paris, Sér. I 305, 159--162 (1987; Zbl 0621.10023)