  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. The right endpoint is $\pm b/2$, or $(b-1)/2$, depending on the
analytic properties of the automorphic $L$-functions attached to $\tau$. We
study the automorphic forms $\Phi_{i}^{(b)}$ obtained as residues at the points
$s_i^{(b)}$ (defined precisely in the paper) by calculating their cuspidal
exponents in certain cases. In the case of the "endpoint" $s_0^{(b)}$ and
`first interior point' $s_1^{(b)}$ in the segment of singularity points, we are
able to determine a set containing \textit{all possible} cuspidal exponents of
$\Phi_0^{(b)}$ and $\Phi_1^{(b)}$ precisely for all $a$ and $b$. In these
cases, we use the result of the calculation to deduce that the residual
automorphic forms lie in $L^2(G(k)\backslash G(\mathbf{A}))$. In a more precise
sense, our result establishes a relationship between, on the one hand, the
actually occurring cuspidal exponents of $\Phi_i^{(b)}$, residues at interior
points which lie to the right of the origin, and, on the other hand, the
"analytic properties" of the original residual-data Eisenstein series at the
origin. This preprint is a longer version of the paper "Analytic Properties of
Residual Eisenstein Series, I", with the details of some proofs added and some
additional examples adduced in support of the main conjecture.
