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The idea of the metaplectic theta function was introduced by Tomio Kubota inthe 1960s. These theta functions are constructed as residues of Eisensteinseries and are only known completely in the case of double covers and, up tothe ambiguity of a constant, for triple covers. In 1992 Jeff Hoffsteinpublished formulae by which these can be computed in certain cases over arational function field. The author gave an alternative approach in 2007. Bothof these methods give the coefficients in a closed form. The rational functionfield is unusual in that it has a large automorphism group. In this paper weshow that this group has an operation on the coefficients. This operation isnot visible from the explicit formulae.

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