  Let $G$ be a linear split algebraic group. The degenerate Eisenstein series
associated to a maximal parabolic subgroup $E_{P}(f^{0},s,g)$ with the
spherical section $f^{0}$ is studied in the first part of the thesis. In this
part, we study the poles of $E_{P}(f^{0},s,g)$ in the region $\operatorname{Re}
s >0$. We determine when the leading term in the Laurent expansion of
  $E_{P}(f^{0},s,g)$ around $s=s_0$ is square integrable. The second part is
devoted to finding identities between the leading terms of various Eisenstein
series at different points. We present an algorithm to find this data and
implement it on \textit{SAGE}. While both parts can be applied to a general
algebraic group, we restrict ourself to the case where $G$ is split exceptional
group of type $F_4,E_6,E_7$, and obtain new results.
