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Terms in the Selberg trace formula for ${\rm SL}(3,{\bf Z})\backslash {\rm SL}(3,{\bf R})/{\rm SO}(3,{\bf R})$ associated to Eisenstein series coming from a maximal parabolic subgroup

Terms in the Selberg trace formula for ${\rm SL}(3,{\bf Z})\backslash {\rm SL}(3,{\bf R})/{\rm SO}(3,{\bf R})$ associated to Eisenstein series coming from a maximal parabolic subgroup

There are two types of Eisenstein series associated to <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper S normal upper L left-parenthesis 3 comma bold upper Z right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">S</mml:mi> <mml:mi mathvariant="normal">L</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mn>3</mml:mn> <mml:mo>,</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="bold">Z</mml:mi> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathrm {SL}(3, …