English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

First we explain the concept of local deformation over a 'parameter' algebraP, in particular the notion of a P-lattice in a Lie group. Purpose of thisarticle is to define the spaces of automorphic resp. cusp forms on the upperhalf plane H for a P- (!) lattice of SL(2, R) and to investigate theirstructure. It turns out that in almost all cases these spaces are free modulesover the complexified P of rank equal to the dimension of the spaces ofautomorphic resp. cusp forms for the body, which is the associated ordinarylattice in SL(2, R) . In other words almost every automorphic resp. cusp formadmits an 'adaption' to local deformations of the lattice. This is shown bygiving the quotient of H by the P-lattice together with the cusps the structureof a P- Riemann surface and writing the spaces of automorphic resp. cusp formsas global sections of holomorphic P- (!) line bundles on this quotient.

Stability of the space of Automorphic Forms under Local Deformations of the Lattice