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Results tagged with automorphic-forms
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user 95002
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.
3
votes
Rankin-Selberg integral for GL(3) form with Odd Maass form on GL(2)
Like Peter Humphries suggests, you need to replace u with $\Lambda_2 u$ and replace $F$ with something that transforms appropriately on the upper-left copy of SO(2).
Thinking of the weight 2 raise $\ …
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1
vote
Bound of higher rank spherical Whittaker function
Roughly $GL(n) = R^\times SL(n)$, and your example on n=2 is only winning in the $R^\times$ part of the Whittaker function. For the $SL(n)$ Whittaker function, say $\mu=r+\mu^*$ where the coordinates …
- 151
3
votes
0
answers
271
views
Spectral decomposition on GL(n)
If $\Delta_1, \ldots, \Delta_{n-1}$ are a basis of the ring of commuting bi-$SL(n,R)$-invariant differential operators, $L_0^2=L_0^2(SL(n,Z)\backslash SL(n,R))$ is the space of cuspidal automorphic fu …
- 151
2
votes
On an inequality about asymptotics of Whittaker functions
Not sure about the level of generality in Wallach's paper, but if that Whittaker function is given by a Jacquet integral (Multiplicity One for Whittaker functions), you can integrate by parts many tim …
- 151
0
votes
Antiholomorphic cusp forms of negative weight
It's reasonable to assume that he means $S_{-k}(\Gamma) = \overline{S_k(\Gamma)}$ for $k > 0$. So $k \ge 2$ are holomorphic and $k \le -2$ are antiholomorphic. If you treat them all as Maass forms w …
- 151
3
votes
Automorphic forms on GL(3)
Slightly old question, but: There are Maass forms on GL(3) whose minimal K-type is non-spherical. There is a paper of Miyazaki on the (g,K) module structure of GL(3), and I'm working on a more compl …
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