The Fourier coefficients of metaplectic theta series on GL(2) over rational function fields

Original · EN

The idea of the metaplectic theta function was introduced by Tomio Kubota in the 1960s. These theta functions are constructed as residues of Eisenstein series and are only known completely in the case of double covers and, up to the ambiguity of a constant, for triple covers. In 1992 Jeff Hoffstein published formulae by which these can be computed in certain cases over a rational function field. The author gave an alternative approach in 2007. Both of these methods give the coefficients in a closed form. The rational function field is unusual in that it has a large automorphism group. In this paper we show that this group has an operation on the coefficients. This operation is not visible from the explicit formulae.