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Results tagged with automorphic-forms
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An automorphic form is a well-behaved function from a topological group $G$ to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup $\Gamma \subset G$ of the topological group. Automorphic forms are a generalization of the idea of periodic functions in Euclidean space to general topological groups.
9
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Geometric interpretation of Cusps for general groups?
Let $\mathrm{G}$ be a reductive group over a number field $F$, but for simplicity we can think about $\mathrm{G}=\mathrm{GL_n}$ for $n>2$ and $F =\mathbb{Q}$.
Then for an automorphic form,
$\varphi …
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13
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Euler Subgroups and Automorphic L-functions
Recently, I have read about the Whittaker expansion for $\mathrm{GL}_n$ and was struck by the utility of the mirabolic subgroup, $\mathrm{P}_n\subset \mathrm{GL}_n$ of matrices with bottom row $(0\; 0 …
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Underlying idea for (automorphic) L-function?
Edit: So with a few more months of math under my belt, I recognize some of the issues with this question. I still hope for an answer, so let me say a few things.
Within the Langlands philosophy, L-fu …
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3
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Using the Hilbert symbol to find nice field extensions
Let $p$ and $q$ be (not necessarily distinct) odd primes and let $F=\mathbb{Q}_p(\mu_q)$. The $q^{th}$ Hilbert symbol induces a non-degenerate alternating form $$(\cdot,\cdot)_q:F^\times/(F^\times)^q\ …
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6
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Reduction to Lie algebra version of fundamental lemma?
Ngo famously proved the Langlands-Shelstad fundamental lemma for Lie algebras using the geometry of the Hitchin fibration.
For the purposes of the trace formula, one actually needs the fundamental le …
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14
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Primer on Eisenstein series
My apologies if this question is a duplicate. I seached, and the closest I could locate is this question, which has very intriguing and intractable (for me) responses.
In my continuing journey of ent …
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