arXiv subjects

Joachim Hilgert

Publications and source records attributed to Joachim Hilgert.

40 records · Page 3Linked to original sources

arXiv2007

Meromorphic continuation of dynamical zeta functions via transfer operators

We describe a general method to prove meromorphic continuation of dynamical zeta functions to the entire complex plane under the condition that the corresponding partition functions are given via a dynamical trace formula from a family of transfer operators. Further we give general conditions for the partition functions associated with general spin chains to be of this type and provide various families of examples for which these conditions are satisfied. Keywords: Dynamical zeta function, transfer operator, trace formulae, thermodynamic formalism, spin chain, Fock space, regularized determinants, weighted composition operator.

math.FA↗

arXiv2005

Cohomology of arithmetic groups with infinite dimensional coefficient spaces

The cuspidal cohomology groups of arithmetic groups in certain infinite dimensional Modules are computed. As a result we get a simultaneous generalization of the Patterson-Conjecture and the Lewis-Correspondence.

math.NT↗

arXiv2004

The Lewis Correspondence for submodular groups

The Lewis Correspondence attaching a unique "period function" to each Maass wave form for SL(2,Z) is extended to subgroups of finite index. This is achieved by using vector-valued forms.

math.NT↗

arXiv2002

Transfer operators and dynamical zeta functions for a class of lattice spin models

We investigate the location of zeros and poles of a dynamical zeta function arizing in a class of lattice spin models introduced in the 60-ties by M. Kac. The transfer operator method allows us to prove the xistence of infinitely nontrivial zeros of this function on the real line. For certain parameter values there exist also infinitely many trivial equally spaced zeros on a line parallel to the imaginary axis. Hence also for this kind of dynamical zeta function some kind of Riemann hypothesis seems to hold.

math.DS↗