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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Sp(2,IR) of the usual symplectic group Sp(2,IR) (matrix size four) from those of its compact twist Sp(2) = Sp(2, C) n U(4) (U(4): the unitary group of size four). Our main point is that this construction preserves L functions. As well known, we have 5/?(2)/{±1} = 5 (5), and (SO(5), Sp(2, P)) form a dual reductive pair defmed by Howe [9], so such construction is naturally expected. Actually, one could omit Sp(2) and give a formulation only on SO (5), but we did not do so. For example, we formulate Hecke theory on Sp (2), and not on SO (5). This is because we have the following motivation. By Ihara [13] or Langlands [20], it has been conjectured that there should exist some good correspondence between automorphic forms of Sp (n) and Sp(n,IR). When n = l, this is Eichler's classical theorem. For « = 2, some examples and some good dimensional relations between these forms have been known (cf. [8], [10], [11], [12]). The only method to prove such conjecture seems to be the trace formula. It has worked well at least for dimensional relations (loc. cit.). But a more direct correspondence, if it exists, would be also very interesting. Here, instead of passing from Sp(2) to 5/7 (2, P),

Construction of half integral weight Siegel modular forms of Sp (2, R) from automorphic forms of the compact twist Sp (2).