A Riemann Hypothesis Condition for Metaplectic Eisenstein Series
نویسنده
چکیده
Let A be the adeles of the function eld Fq (T). If E(g; s) is the Eisenstein series associated with the spherical vector in the principal series representation of the double cover of GL2(A), then the Fourier coeecients (Whittaker functions) of E(g; s) have an Euler product and satisfy a `Riemann Hypothesis' condition. Namely, the zeros occur only on the line <(s) = 0. These Whittaker functions are essentially qua-dratic L-functions associated with hyperelliptic curves. This result adds to the list of known examples for which the Fourier coeecients of Eisenstein series coming from the spherical vector in the principal series representation satisfy a Riemann Hypothesis condition.
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تاریخ انتشار 1997