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Equality cases for condenser capacity inequalities under symmetrization

Dimitrios Betsakos, Stamatis Pouliasis (2012)

Annales UMCS, Mathematica

It is well known that certain transformations decrease the capacity of a condenser. We prove equality statements for the condenser capacity inequalities under symmetrization and polarization without connectivity restrictions on the condenser and without regularity assumptions on the boundary of the condenser.

Équations diophantiennes polynomiales à hautes multiplicités

Michel Langevin (2001)

Journal de théorie des nombres de Bordeaux

On montre comment écrire de grandes familles, avec de hautes multiplicités, de cas d’égalité A + B = C pour l’inégalité de Stothers-Mason (si A ( X ) , B ( X ) , C ( X ) sont des polynômes premiers entre eux, le nombre exact de racines du produit A B C dépasse de 1 le plus grand des degrés des composantes A , B , C ) . On développera pour cela des techniques polynomiales itératives inspirées des décompositions de Dunford-Schwartz et de fonctions de Belyi. Des exemples d’application avec les conjectures ( a b c ) ou de M. Hall sont développés.

Ergodic theory of interval exchange maps.

Marcelo Viana (2006)

Revista Matemática Complutense

A unified introduction to the dynamics of interval exchange maps and related topics, such as the geometry of translation surfaces, renormalization operators, and Teichmüller flows, starting from the basic definitions and culminating with the proof that almost every interval exchange map is uniquely ergodic. Great emphasis is put on examples and geometric interpretations of the main ideas.

Ergodic Universality Theorems for the Riemann Zeta-Function and other L -Functions

Jörn Steuding (2013)

Journal de Théorie des Nombres de Bordeaux

We prove a new type of universality theorem for the Riemann zeta-function and other L -functions (which are universal in the sense of Voronin’s theorem). In contrast to previous universality theorems for the zeta-function or its various generalizations, here the approximating shifts are taken from the orbit of an ergodic transformation on the real line.

Currently displaying 101 – 120 of 250