Archimedean newform theory for $\operatorname{GL}_n$

Representation theory for linear algebraic groups (20G05) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45) Representations of Lie and linear algebraic groups over local fields (22E50) Representation-theoretic methods; automorphic representations over local and global fields (11F70)

Cites Work

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The Archimedean zeta integrals for $\mathrm{GL}(3)\times \mathrm{GL}(2)$
Spherical harmonics and approximations on the unit sphere. An introduction
Gross-Zagier formula for $\text{GL}_ 2$.
On explicit integral formulas for $\text{GL}(n, \mathbb R)$-Whittaker functions. With an appendix by Daniel Bump, Solomon Friedberg, and Jeffrey Hoffstein
Whittaker newforms for archimedean representations of GL(2)
Function theory in the unit ball of ${\mathbb{C}}^ n$
Automorphic induction for $\text{GL}(n,\mathbb C)$
Baxter operator and archimedean Hecke algebra
Calculus of principal series Whittaker functions on $\text{GL}(3,\mathbb C)$
Explicit constructions of automorphic $L$-functions
Conducteur des représentations du groupe linéaire
Representations of real reductive Lie groups
Young tableaux, Gelfand patterns, and branching rules for classical groups
Archimedean $L$-factors on $\text{GL}(n)\times\text{GL}(n)$ and generalized Barnes integrals
The local zeta integrals for $\mathrm{GL}(2,\mathbb{C})\times \mathrm{GL}(2,\mathbb{C})$
Archimedean Godement-Jacquet zeta integrals and test functions
Archimedean zeta integrals for the exterior square $L$-functions on $\mathrm{GL}_{n}$
Explicit calculations with Eisenstein series
Lectures on automorphic $L$-functions
Automorphic induction for $GL(n)$ (over local nonarchimedean fields)
Mellin transforms of Whittaker functions on $\text{GL} (4,\mathbb{R})$ and $\text{GL} (4,\mathbb{C})$
A correction to ``Conducteur des représentations du groupe linéaire
Smooth Fréchet globalizations of Harish-Chandra modules
Analytic properties of spherical cusp forms on $\mathrm{GL}(n)$
Test vectors for Rankin-Selberg $L$-functions
Derivatives for smooth representations of $\mathrm{GL}(n, \mathbb R)$ and $\mathrm{GL}(n, \mathbb C)$
Some results on Archimedean Rankin-Selberg integrals
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Godement-Jacquet integrals on $\mathrm{GL}(n,\mathbb{C})$
Essential Whittaker functions for $\mathrm{GL}(n)$
Whittaker functions associated to newforms for $GL(n)$ over $p$-adic fields
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Hecke operators on $\Gamma_0(m)$
Automorphic forms on GL (2)
On some results of Atkin and Lehner
Automorphic forms on $\mathrm{GL}(2)$. Part II
Zeta functions of simple algebras
Mellin transforms of GL ( n , [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /) whittaker functions]
Rankin-Selberg Convolutions
Transcending Classical Invariant Theory
Old Forms on GL n
On irreducibility of standard modules for generic representations
Parity preservation of $K$-types under theta correspondence
TEST VECTORS FOR LOCAL CUSPIDAL RANKIN–SELBERG INTEGRALS
Test vectors for non‐Archimedean Godement–Jacquet zeta integrals
A template method for Fourier coefficients of Langlands Eisenstein series
Calculus of archimedean Rankin–Selberg integrals with recurrence relations
Periods of automorphic forms: the case of
Integral moments of L-functions
Fonctions de Whittaker associées aux groupes de Chevalley
The local period integrals and essential vectors
Test vectors for Archimedean period integrals
The newform $K$-type and $p$-adic spherical harmonics

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Archimedean newform theory for \(\operatorname{GL}_n\)