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Uniformization of triangle modular curves.

Pilar Bayer, Artur Travesa (2007)

Publicacions Matemàtiques

In the present article, we determine explicit uniformizations of modular curves attached to triangle Fuchsian groups with cusps. Their Hauptmoduln are obtained by integration of non-linear differential equations of the third order. Series expansions involving integral coefficients are calculated around the cusps as well as around the elliptic points. The method is an updated form of a differential construction of the elliptic modular function j, first performed by Dedekind in 1877. Subtle differences...

Unramified Skolem problems and unramified arithmetic Bertini theorems in positive characteristic.

Tamagawa, Akio (2003)

Documenta Mathematica

Variation of periods modulo $p$ in arithmetic dynamics.

Silverman, Joseph H. (2008)

The New York Journal of Mathematics [electronic only]

Variations on a theme of Runge: effective determination of integral points on certain varieties

Aaron Levin (2008)

Journal de Théorie des Nombres de Bordeaux

We consider some variations on the classical method of Runge for effectively determining integral points on certain curves. We first prove a version of Runge’s theorem valid for higher-dimensional varieties, generalizing a uniform version of Runge’s theorem due to Bombieri. We then take up the study of how Runge’s method may be expanded by taking advantage of certain coverings. We prove both a result for arbitrary curves and a more explicit result for superelliptic curves. As an application of our...

Weak approximation and non-abellian fundamental groups

D. Harari (2000)

Annales scientifiques de l'École Normale Supérieure

Zéro-cycles de degré 1 sur les solides de Poonen

Jean-Louis Colliot-Thélène (2010)

Bulletin de la Société Mathématique de France

B. Poonen a récemment exhibé des exemples de variétés projectives et lisses de dimension 3 sur un corps de nombres qui n’ont pas de point rationnel et pour lesquelles il n’y a pas d’obstruction de Brauer–Manin après revêtement fini étale. Je montre que les variétés qu’il construit possèdent des zéro-cycles de degré 1.

Zero-cycles on quadric fibrations: Finiteness theorems and the cycle map.

R. Parimala, V. Suresh (1995)

Inventiones mathematicae

Zero-cycles on quadric fibrations: Finiteness theorems and the cycle map (Erratum).

R. Parimala, V. Suresh (1996)

Inventiones mathematicae

Displaying 101 – 108 of 108

Currently displaying 101 – 108 of 108