## Abstract

Kubota [*T. Kubota*, Some results concerning reciprocity law and real analytic automorphic functions, in: 1969 Number Theory Institute (Proc. Sympos. Pure Math. XX, State Univ. New York, Stony Brook, N.Y., 1969), Amer. Math. Soc., Providence, R.I. (1971), 382–395.] showed how the theory of Eisenstein series on the higher metaplectic covers of SL_{2} (which he discovered) can be used to study the analytic properties of Dirichlet series formed with *n*-th order Gauss sums. In this paper we will prove a functional equation for such Dirichlet series in the precise form required by the companion paper [*B. Brubaker, D. Bump, G. Chinta, S. Friedberg*, and *J. Hostein*, Weyl group multiple Dirichlet series I, preprint, http://sporadic.stanford.edu/bump/wmd.pdf.]. Closely related results are in Eckhardt and Patterson [*C. Eckhardt* and *S. J. Patterson*, On the Fourier coefficients of biquadratic theta series, Proc. London Math. Soc. (3) **64**(2) (1992), 225–264.].

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