Quelques remarques sur des questions d'approximation diophantienne

Patrice Philippon

Type: Article

Publication Date: 1999-04-01

Citations: 15

DOI: https://doi.org/10.1017/s0004972700032937

Abstract

Hoping for a hand-shake between methods from diophantine approximation theory and transcendance theory, we show how zeros estimates from transcendance theory imply Roth's type lemmas (including the product theorem). We also formulate some strong conjectures on lower bounds for linear forms in logarithms of rational numbers with rational coefficients, inspired by the subspace theorem and which would imply, for example, the abc conjecture.

Locations

Bulletin of the Australian Mathematical Society - View - PDF

Similar Works

Action	Title	Year	Authors
+	Open Diophantine Problems	2003	Michel Waldschmidt
+	Diophantine approximation	2021	Noriko Hirata-Kohno
+	Approximations Diophantiennes et Nombres Transcendants. Diophantine Approximations and Transcendental Numbers	1992	Patrice Philippon
+ PDF Chat	Transcendental Numbers and Diophantine Approximations	2000	Serge Lang
+	Transcendental Numbers and Diophantine Approximations	1971	Serge Lang
+ PDF Chat	Transcendental numbers and diophantine approximations	1971	Serge Lang
+ PDF Chat	Diophantine approximation and transcendental number theory	1988	Guang Shan Xu
+	A $p$-adic lower bound for a linear form in logarithms	2021	Neea Palojärvi Louna Seppälä
+	Diophantine approximations in the field of p-adic numbers	1984	Yu. V. Nesterenko
+	A $p$-adic lower bound for a linear form in logarithms	2021	Neea Palojärvi Louna Seppälä
+	Tools from Diophantine approximation and transcendence theory	2015	Jan‐Hendrik Evertse Kálmán Győry
+	Transcendence and Diophantine approximation	2010	Boris Adamczewski Yann Bugeaud
+ PDF Chat	Diophantine approximation and the subspace theorem	2025	Shivani Goel Rashi Lunia Anwesh Ray
+	Diophantine analysis and related fields	2010	尚夫小松
+ PDF Chat	None	2002	Yann Bugeaud
+ PDF Chat	Addendum à quelques remarques sur des questions d'approximation diophantienne	2000	Patrice Philippon
+ PDF Chat	A p-adic lower bound for a linear form in logarithms	2022	Neea Palojärvi Louna Seppälä
+	Diophantine approximation in terms of linear reccurring sequences	1994	Peter J. Grabner
+	On a Problem of Mahler Concerning the Approximation of Exponentials and Logarithms	2000	Michel Waldschmidt
+	On a problem of Mahler concerning the approximation of exponentials and logarithms	2000	Michel Waldschmidt

Works That Cite This (13)

Action	Title	Year	Authors
+ PDF Chat	Addendum à quelques remarques sur des questions d'approximation diophantienne	2000	Patrice Philippon
+ PDF Chat	None	2002	Yann Bugeaud
+ PDF Chat	Elliptic logarithms, diophantine approximation and the Birch and Swinnerton-Dyer conjecture	2014	Vincent Bosser Andrea Surroca
+ PDF Chat	Équations diophantiennes polynomiales à hautes multiplicités	2001	M. Langevin
+ PDF Chat	Sur le théorème du produit	2001	Gaël Rémond
+	Open Diophantine Problems	2004	Michel Waldschmidt
+	Points on Curves	2020	Levent Alpöge
+	Perfect Powers: Pillai's works and their developments	2009	Michel Waldschmidt
+	Some observations on familiar numbers	2002	Daniel Richardson Simon Langley
+	Lecture on the abc Conjecture and Some of Its Consequences	2014	Michel Waldschmidt

Works Cited by This (9)

Action	Title	Year	Authors
+	Elliptic Curves: Diophantine Analysis	1978	Serge Lang
+ PDF Chat	An explicit version of Faltings' Product Theorem and an improvement of Roth's lemma	1995	Jan‐Hendrik Evertse
+ PDF Chat	Nouveaux Lemmes de Zéros dans les Groupes Algébriques Commutatifs	1996	Patrice Philippon
+	The2-adic Thue-Siegel-Roth-Schmidt theorem	1977	Hans Peter Schlickewei
+	Diophantine Approximation on Abelian Varieties	1991	Герд Фалтингс
+ PDF Chat	Multiplicity estimates and the product theorem	1995	Michael Nakamaye
+	The subspace theorem in diophantine approximations	1989	Wolfgang M. Schmidt
+	Elliptic Curves	1978	Serge Lang
+ PDF Chat	Diophantine Approximations and Value Distribution Theory	1987	Paul Vojta