Eliot Brenner

  1. Notes on Analytic Properties of Residual Eisenstein Series, I.

    Authors: Eliot Brenner
    Subjects: Number Theory
    Abstract

    We partially generalize the results of Kudla and Rallis on the poles of
    degenerate, Siegel-parabolic Eisenstein series to residual-data Eisenstein
    series. In particular, for $a,b$ integers greater than 1, we show that poles of
    the Eisenstein series induced from the Speh representation $\Delta(\tau,b)$ on
    the Levi $\mathrm{GL}_{ab}$ of $\mathrm{Sp}_{2ab}$ are located in the "segment"
    of half integers $X_{b}$ between a "right endpoint" and its negative, inclusive
    of endpoints.

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