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Let $G$ be a linear split algebraic group. The degenerate Eisenstein seriesassociated to a maximal parabolic subgroup $E_{P}(f^{0},s,g)$ with thespherical section $f^{0}$ is studied in the first part of the thesis. In thispart, 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 isdevoted to finding identities between the leading terms of various Eisensteinseries at different points. We present an algorithm to find this data andimplement it on \textit{SAGE}. While both parts can be applied to a generalalgebraic group, we restrict ourself to the case where $G$ is split exceptionalgroup of type $F_4,E_6,E_7$, and obtain new results.

Poles of degenerate Eisenstein series and Siegel-Weil identities for exceptional split groups