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GL(n) × GL(n) × … × GL(n) Examples

, 2012
This chapter investigates the question which begings as follows. Suppose we have a geometrically irreducible middle extension sheaf G on 𝔾ₘ/k which is pure of weight zero, such that the object N := G(1/2)[1] ɛ Garith is “dimension” n and has Gsubscript geom,N = Garith,N = GL(n). Suppose in addition we are given s ≤ 2 distinct characters χ‎ᵢ of kˣ.
Nicholas M. Katz
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Archimedean zeta integrals on GL n × GL m and SO2n+1 × GL m

Manuscripta Mathematica, 2012
In this paper, we evaluate archimedean zeta integrals for automorphic L-functions on GL n × GL n-1+l and on SO2n+1 × GL n+l , for l = −1, 0, and 1.
Taku Ishii, Eric Stade
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Bispectral and $(\mathfrak{gl}_{N},\mathfrak{gl}_{M})$ dualities

Functional Analysis and Other Mathematics, 2007
Let \(V=\langle p_{ij}(x)e^{\lambda_i x}, i = 1, \dots, n, j =1, \dots, N_i \rangle\) be a space of quasipolynomials of dimensions \(N = N_1 + \dots, N_n\). Then, the regularized fundamental operator of \(V\) is defined as the polynomial differential operator \(D = \sum_{i=0}^N A_{N-1}(x) \partial^i_x\) annihilating \(V\) and its leading coefficient ...
Mukhin, Evgenii E., Tarasov, Vitaly O., Varchenko, Alexander N.   +2 more
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?????????????????? ???????????? ?????????? ?????????? GL-?????????????? ?????????????????? ???????????????????????????????? ?????????????????????????????????? ???????????? ?? ???????????? ??????????????

2016
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On the growth of cuspidal cohomology of GL(2) and GL(3)

Journal of Number Theory, 2020
Abstract We estimate the growth of cuspidal cohomology of G L 2 ( A Q ) . Quantitatively, we provide bounds on the total number of normalised eigenforms of Hecke operators which are obtained by automorphic induction from Hecke characters of imaginary quadratic fields grows as level structure varies.
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Automorphic Sl₂-Periods and the Subconvexity Problem for Gl₂ × Gl₃

2020
We prove a new (conditional) result toward the subconvexity problem for certain automorphic L-functions for GL₂ × GL₃. This follows from the computation of new SL₂-period integrals associated with newforms f and g of even weight and odd squarefree level.
Pal, Aprameyo, de Vera-Piquero, Carlos
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Rankin-Selberg convolutions for GL(n)×GL(n) and GL(n)×GL(n−1) for principal series representations

Science China Mathematics, 2023
Jian-Shu Li, Dongwen Liu, Feng Su, Binyong Sun   +3 more
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First moments of GL(3)×GL(2) and GL(2)L‐functions and their applications

Mathematische Nachrichten
Abstract Let be a self‐dual Hecke–Maaß form for underlying the symmetric square lift of a ‐newform of square‐free level and trivial nebentypus. In this paper, we are interested in the first moments of the central values of ‐functions and ‐functions.
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Subconvexity for GL(3)×GL(2) twists

Advances in Mathematics, 2022
Prahlad Sharma, Will Sawin
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