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 Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

We continue with our study of the noncritical exceptional zeros of Katz’   $p$  -adic   $L$  -functions attached to a CM field   $K$  , following two threads. In the 1st thread, we redefine our (group-ring-valued)   ${\mathcal {L}}$  -invariant associated with each   ${\mathbb {Z}}_p$  -extension   $K_\Gamma $   of   $K$   in terms of   $p$  -adic height pairings and interpolate them as   $K_\Gamma $   varies to a  universal  (multivariate) group-ring-valued   ${\mathcal {L}}$  -invariant. In the 2nd thread, we use our results to study the exceptional zeros of the Rankin–Selberg   $p$  -adic   $L$  -functions at noncritical specializations of the self-products of nearly ordinary CM families, via the factorization statements we establish. The factorization theorems are extensions of the results due to Greenberg and Palvannan.

ℒ-Invariants, p -Adic Heights, and Factorization of p -Adic L -Functions