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The meaning of $L_{\chi}^2(G(\mathbb Q) \backslash G(\mathbb A)^1)$
I'm reading James Arthur's notes on the trace formula and am confused on a point on pages 65 and 66. For $G$ a reductive group over $\mathbb Q$ we are going over the decomposition of the space $L^2(G(...
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The kernel $K(x,y)$ as an integral over Eisenstein series for $\operatorname{GL}_2$
Let $G = \operatorname{GL}_2$, $f \in C_c^{\infty}(G(\mathbb A)/Z(\mathbb A))$, and $V = L^2( G(\mathbb Q)Z(\mathbb A)\backslash G(\mathbb A))$ (trivial central character). Then the operator $R(f)$ ...
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