We give a precise determination of the algebraicity critical values L -functions associated to Siegel modular forms half-integral weight and arbitrary degree. generalise improve on similar results for integral-weight case by adapting Rankin-Selberg method this setting, with aid Shimura's theory recent work Bouganis. An essential ingredient is proof new analogue Garrett's conjecture Klingen Eise...

This paper studies spherical Whittaker functions for central extensions of reductive groups over local fields. We follow the development of Chinta-Offen to produce a metaplectic Casselman-Shalika formula for tame covers of all unramified groups.