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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.
4
votes
Accepted
On the Saito Kurokawa representation
Under the isomorphism $\mathrm{PGSp}(4) \cong \mathrm{SO}(5)$ the Saito-Kurokawa representation corresponds to a Siegel modular form. In particular its archimedean component is in the holomorphic disc …
- 40.2k
29
votes
What automorphic forms are expected to occur in the zeta function of moduli space of curves?
I can tell you the complete answer for $g \leq 2$:
When $g=0$ and $n \geq 3$ no nontrivial automorphic forms appear.
When $g=1$ and $n \geq 1$ the class of automorphic forms which appear are exact …
- 40.2k
6
votes
Philosophy behind cohomological representations
I'm far from an expert, but here is a comment. In the case of a Shimura variety, the Matsushima-Murakami formula and the (proof of the) Zucker conjecture shows that cohomological representations are p …
- 40.2k
5
votes
Accepted
A frustrating cohomology class on the moduli of abelian surfaces
The answer to the main question above is indeed positive: the restriction map is nonzero for all $k \geq 2$. This was proved in Section 5 of my paper Tautological rings of spaces of pointed genus two …
- 40.2k