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

Let K be an imaginary quadratic field of discriminant -D_K<0. We introduce anotion of an adelic Maass space S_{k, -k/2}^M for automorphic forms on thequasi-split unitary group U(2,2) associated with K and prove that it is stableunder the action of all Hecke operators. When D_K is prime we obtain aHecke-equivariant descent from S_{k,-k/2}^M to the space of elliptic cusp formsS_{k-1}(D_K, \chi_K), where \chi_K is the quadratic character of K. For a given\phi \in S_{k-1}(D_K, \chi_K), a prime l >k, we then construct (mod l)congruences between the Maass form corresponding to \phi and hermitian modularforms orthogonal to S_{k,-k/2}^M whenever the l-adic valuation ofL^{alg}(\Sym^2 \phi, k) is positive. This gives a proof of the holomorphicanalogue of the unitary version of Harder's conjecture. Finally, we use thesecongruences to provide evidence for the Bloch-Kato conjecture for the motives\Sym^2 \rho_{\phi}(k-3) and \Sym^2 \rho_{\phi}(k), where \rho_{\phi} denotesthe Galois representation attached to \phi.

Maass spaces on U(2,2) and the Bloch-Kato conjecture for the symmetric square motive of a modular form