# Questions tagged [automorphic-forms]

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.

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### Question on the proper sub-representation of induced representation

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### The Fontaine Mazur conjecture for $\text{GL}_1$ over $\mathbf{Q}$

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### Level vs. conductor of a supercuspidal representation

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### Intertwining operator is not an isomorphism?

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### A question related to newform and irreducible cuspidal representation of $\operatorname{GL}_n$

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### Residual and continuous spectra of $L^2( G(k) \backslash G(\mathbb A) ; \omega)$, and cuspidal automorphic data

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### Global tempered representation vs representation whose global A-parameter is tempered

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### Globally generic automorphic representation is contained in some generic A-packet?

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### Equivalence between Ramanujan and Selberg conjectures

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### A weakly holomorphic modular form is a harmonic maass form

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### Meaning of extended principal part of weakly holomorhpic modular forms

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### Left translation of automorphic form satisfies $K$-finiteness?

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### Restriction of product of automorphic forms

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### Global Arthur packet consist of only globally generic representations?

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### Semidirect product of metaplectic group and Heisenberg group

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### How can I see the relation between shtukas and the Langlands conjecture?

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### Bounds on Fourier coefficients for $GL(3)$

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### Under Ramanujan conjecture, is primitivity equivalent to cuspidality and irreducibility?

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### Is an automorphic form of $\operatorname{GL}_{n}(\mathbb{A}_{\mathbb{Q}})$ determined by its L-function?

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### Degree of automorphic forms, SL(3,Z), and the elliptic Gamma function

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### Iwasawa decomposition on unitary group of anisotropic kernel

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### Metaplectic group $Mp(2n)(\mathbb{A}_F)$ splits over $Sp(2n)(F)$?

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### Sets of L-functions being “almost bimonoids”

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### Do we know absolute bounds for the norm of Satake parameters?

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### Paramodular forms with level and Iwahori subgroups?

**5**

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### Intuition about how Voronoi formulas change lengths of sums

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### Subquotient of principal series

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### Distribution of signs of automorphic forms

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### Relations between spectral parameters of automorphic representations

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### For what automorphic representations is Ramanujan-Petersson known?

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### Jacquet module of irreducible principal series

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### Jacquet module of unramified principal series representaion with respect to parabolic subgroup of $GL_n(F)$

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### Some question on parabolic induction

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### Irreducibility of parabolic induction on unitary group

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### Central character of some conjugate self dual representation

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### Analogous theorem for Hilbert modular forms

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### Are the L-functions of a normalized newform and the corresponding cuspidal representation equal?

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### Rankin-Selberg convolution and product of degrees as of Christmas 2019

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### Conductor of Principal series representation

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### conductor formula

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### Conductor formula for symmetric square transfer

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### Is weakly holomorphic modular form finitely generated as module of modular function?

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### Does the symmetric square L-function vanish at one?

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### Modular form attached to a hecke character of cubic/quartic extension of rational numbers

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### Proving automorphy of the Galois representations of number fields without considering the residual representation

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### Why is Langlands functoriality usually related with period integral in a third group?

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### Double quotients and the isomorphism theorems

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### Fundamental lemma and transfer of characteristic functions of congruent subgroups

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### Archimedean L-factors for symplectic group

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