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 prove algebraicity results for critical $L$-values attached to the group$\text{GSp}_4 \times \text{GL}_2$, and for Gan--Gross--Prasad periods which areconjecturally related to central $L$-values for $\text{GSp}_4 \times\text{GL}_2 \times \text{GL}_2$. Our result for $\text{GSp}_4 \times\text{GL}_2$ gives a new proof (by a very different method) of a recent resultof Morimoto, and will be used in a sequel paper to construct a new $p$-adic$L$-function for $\text{GSp}_4 \times \text{GL}_2$. The results forGross--Prasad periods appear to be new. A key aspect is the computation ofcertain archimedean zeta integrals, whose $p$-adic counterparts are alsostudied in this note.

Algebraicity of $L$-values for $\text{GSp}_4 \times \text{GL}_2$ and $\text{GSp}_4 \times \text{GL}_2 \times \text{GL}_2$