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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.

Essential norms of weighted composition operators on the space of Dirichlet series

Pascal Lefèvre (2009)

Studia Mathematica

We estimate the essential norm of a weighted composition operator relative to the class of Dunford-Pettis operators or the class of weakly compact operators, on the space of Dirichlet series. As particular cases, we obtain the precise value of the generalized essential norm of a composition operator and of a multiplication operator.

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