Abstract After an overview of uses and explorations minimal automorphic ordered sets, we present a criterion when certain superpositions crowns are automorphic. A key lemma to exclude retracts can also be applied sets recently presented in Schröder (Order, https://doi.org/10.1007/s11083-021-09574-3 , 2021).

We characterize the space of the so-called planar mixed automorphic forms of type (ν, μ) with respect to an equivariant pair (ρ, τ) as the image of the usual automorphic forms by an appropriate transform and we investigate some concrete basic spectral properties of a magnetic Schrödinger operator acting on them. The associated polynomials constitute classes of generalized complex polynomials of...

The cohomology of an arithmetic group is built out of certain automorphic forms. This allows computational investigation of these automorphic forms using topological techniques. We discuss recent techniques developed for the explicit computation of the cohomology of congruence subgroups of GL2 over CM-quartic and complex cubic number fields as Hecke-modules.

For a cuspidal automorphic representation Π of GL(4, A), H. Kim proved that the exterior square transfer ∧Π is nearly an isobaric automorphic representation of GL(6, A). In this paper we characterize those representations Π for which ∧Π is cuspidal.

In this article we define the concept of weighted pseudo almost automorphic sequence, and establish some basic properties of these sequences. Further, as an application, we show the existence, uniqueness and global attractivity of weighted pseudo almost automorphic sequence solutions of a neural network model.

We describe the structure of a free loop of rank n in the variety of automorphic Moufang loops as a subdirect product of a free group and a free commutative Moufang loop, both of rank n. In particular, the variety of automorphic Moufang loops is the join of the variety of groups and the variety of commutative Moufang loops.