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 primary objective of this paper is the study of different instances ofthe elliptic Stark conjectures of Darmon, Lauder and Rotger, in a situationwhere the elliptic curve attached to the modular form $f$ has splitmultiplicative reduction at $p$ and the arithmetic phenomena are speciallyrich. For that purpose, we resort to the principle of improved $p$-adic$L$-functions and study their $\mathcal L$-invariants. We further interpretthese results in terms of derived cohomology classes coming from the setting ofdiagonal cycles, showing that the same $\mathcal L$-invariant which arises inthe theory of $p$-adic $L$-functions also governs the arithmetic of Eulersystems. Thus, we can reduce, in the split multiplicative situation, theconjecture of Darmon, Lauder and Rotger to a more familiar statement abouthigher order derivatives of a triple product $p$-adic $L$-function at a pointlying inside the region of classical interpolation, in the realm of the morewell-known exceptional zero conjectures.

Generalized Kato classes and exceptional zero conjectures