Algebraicity of metaplectic L-functions

We give a precise determination of the algebraicity of the critical values of L-functions associated to Siegel modular forms of half-integral weight and arbitrary degree. We generalise and improve on similar results for the integral weight case by adapting the Rankin-Selberg method to this setting, with the aid of Shimura's theory of half-integral weight modular forms and recent work on precise algebraicity results by Bouganis. An essential ingredient of this work is a proof of a new analogue of Garrett's conjecture on the algebraicity of Klingen Eisenstein series, a result which is also of independent interest. (c) 2020 Elsevier Inc. All rights reserved.