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

The purpose of this article is proving the equality of two natural   L  ‐invariants attached to the adjoint representation of a weight one cusp form, each defined by purely analytic, respectively, algebraic means. The proof departs from Greenberg's definition of the algebraic   L  ‐invariant as a universal norm of a canonical    Z  p   ‐extension of    Q  p    associated to the representation. We relate it to a certain    2  ×  2    regulator of   p  ‐adic logarithms of global units by means of class field theory, which we then show to be equal to the analytic   L  ‐invariant computed in Rivero and Rotger [ J. Eur. Math. Soc ., to appear].

On the L ‐invariant of the adjoint of a weight one modular form