On some metaplectic Eisenstein series (Q1608610)

The author uses methods developed by N. V. Proskurin to study a certain class of metaplectic Eisenstein series on a suitable subgroup of \(\text{Sp}_4 (\mathbb{Z}[\omega])\) where \(\omega= e^{2\pi i/3}\). Whereas Proskurin studied those Eisenstein series that are either associated with a minimal parabolic subgroup or with a metaplectic theta function associated with a subgroup of \(\text{SL}_2 (\mathbb{Z}[\omega])\) the author here studies Eisenstein series associated with arbitrary metaplectic forms on a subgroup of \(\text{SL}_2 (\mathbb{Z}[\omega])\). The coefficients of the Fourier coefficients of the Eisenstein series are Dirichlet series associated with the original forms. The author obtains a relatively simple formula for these Dirichlet series but their meaning, especially with regard to the generalized Shimura correspondence, remains unclear.