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/

Global: Zendy Plus annual

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

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We introduce a new class of combinatorially defined rational functions andapply them to deduce explicit formulae for local ideal zeta functionsassociated to the members of a large class of nilpotent Lie rings whichcontains the free class-2-nilpotent Lie rings and is stable under directproducts. Our results unify and generalize a substantial number of previouscomputations. We show that the new rational functions, and thus also the localzeta functions under consideration, enjoy a self-reciprocity property,expressed in terms of a functional equation upon inversion of variables. Weestablish a conjecture of Grunewald, Segal, and Smith on the uniformity ofnormal zeta functions of finitely generated free class-2-nilpotent groups.

Generalized Igusa functions and ideal growth in nilpotent Lie rings