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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.
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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
???????????????? ???????????????????? ???????????? ?????????????????? ???????????????? ?????????? ?????? ???????????????? GL-??????????????, ???? ???????????????????????? ?????????????? ???????????????????????????? ?????????????????????????????? ?????????????? ???? ?????????? ????????????, ?? ?????????????????????? ?????????????????? ??????????????????
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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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The Ramanujan Conjecture from GL(2) to GL(n)

2012
Ramanujan’s conjectures regarding the τ-function represent part of a larger spectrum of conjectures, first in the setting of automorphic forms attached to GL(2) and generally to GL(n). In this chapter, we trace this development highlighting what is known and what is unknown.
M. Ram Murty, V. Kumar Murty
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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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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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Subconvexity for GL(3)×GL(2) twists

Advances in Mathematics, 2022
Prahlad Sharma, Will Sawin
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