Hezi Halawi
Published 2022-05-12Version 1
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.
On the images and poles of degenerate Eisenstein series for $GL_n(\mathbb A_{\mathbb Q})$ and $GL_n(\mathbb R)$
The Residual Spectrum of $F_4$ Arising from Degenerate Eisenstein Series
The Degenerate Eisenstein Series Attached to the Heisenberg Parabolic Subgroups of Quasi-Split Forms of $Spin_8$
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