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Relevant bibliographies by topics / Langlands-Shahidi method

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Academic literature on the topic 'Langlands-Shahidi method'

Author: Grafiati

Published: 4 June 2021

Last updated: 12 February 2022

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Journal articles on the topic "Langlands-Shahidi method"

1

Asgari, Mahdi. "Local L-Functions for Split Spinor Groups." Canadian Journal of Mathematics 54, no. 4 (August 1, 2002): 673–93. http://dx.doi.org/10.4153/cjm-2002-025-8.

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AbstractWe study the local L-functions for Levi subgroups in split spinor groups defined via the Langlands-Shahidi method and prove a conjecture on their holomorphy in a half plane. These results have been used in the work of Kim and Shahidi on the functorial product for GL2 × GL3.

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2

Kim, Henry H. "On Local L-Functions and Normalized Intertwining Operators." Canadian Journal of Mathematics 57, no. 3 (June 1, 2005): 535–97. http://dx.doi.org/10.4153/cjm-2005-023-x.

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AbstractIn this paper we make explicit all L-functions in the Langlands–Shahidi method which appear as normalizing factors of global intertwining operators in the constant term of the Eisenstein series. We prove, in many cases, the conjecture of Shahidi regarding the holomorphy of the local L-functions. We also prove that the normalized local intertwining operators are holomorphic and non-vaninishing for Re(s) ≥ 1/2 in many cases. These local results are essential in global applications such as Langlands functoriality, residual spectrumand determining poles of automorphic L-functions.

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3

Kim, Wook. "Square Integrable Representations and the Standard Module Conjecture for General Spin Groups." Canadian Journal of Mathematics 61, no. 3 (June 1, 2009): 617–40. http://dx.doi.org/10.4153/cjm-2009-033-3.

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Abstract.In this paper we study square integrable representations and L -functions for quasisplit general spin groups over a p-adic field. In the first part, the holomorphy of L -functions in a half plane is proved by using a variant formof Casselman's square integrability criterion and the Langlands–Shahidi method. The remaining part focuses on the proof of the standard module conjecture. We generalize Muić's idea via the Langlands–Shahidimethod towards a proof of the conjecture. It is used in the work of M. Asgari and F. Shahidi on generic transfer for general spin groups.

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Kim, Henry H. "Langlands-shahidi method and poles of automorphicL-functions II." Israel Journal of Mathematics 117, no. 1 (December 2000): 261–84. http://dx.doi.org/10.1007/bf02773573.

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Shahidi, Freydoon. "Twists of a General Class of L-Functions by Highly Ramified Characters." Canadian Mathematical Bulletin 43, no. 3 (September 1, 2000): 380–84. http://dx.doi.org/10.4153/cmb-2000-045-1.

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AbstractIt is shown that given a local L-function defined by Langlands-Shahidi method, there exists a highly ramified character of the group which when is twisted with the original representation leads to a trivial Lfunction.

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6

Kim, Henry H. "Langlands–Shahidi method and poles of automorphic L-functions III: Exceptional groups." Journal of Number Theory 128, no. 2 (February 2008): 354–76. http://dx.doi.org/10.1016/j.jnt.2007.06.012.

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7

Kim, Henry H. "Langlands-Shahidi Method and Poles of Automorphic L-Functions: Application to Exterior Square L-Functions." Canadian Journal of Mathematics 51, no. 4 (August 1, 1999): 835–49. http://dx.doi.org/10.4153/cjm-1999-036-0.

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AbstractIn this paper we use Langlands-Shahidimethod and the result of Langlands which says that non selfconjugatemaximal parabolic subgroups do not contribute to the residual spectrum, to prove the holomorphy of several completed automorphic L-functions on the whole complex plane which appear in constant terms of the Eisenstein series. They include the exterior square L-functions of GLn, n odd, the Rankin-Selberg L-functions of GLn × GLm, n ≠ m, and L-functions L(s, σ, r), where σ is a generic cuspidal representation of SO10 and r is the half-spin representation of GSpin(10, ). The main part is proving the holomorphy and non-vanishing of the local normalized intertwining operators by reducing them to natural conjectures in harmonic analysis, such as standard module conjecture.

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8

Liu, Baiying. "Genericity of Representations of p-Adic Sp2n and Local Langlands Parameters." Canadian Journal of Mathematics 63, no. 5 (October 18, 2011): 1107–36. http://dx.doi.org/10.4153/cjm-2011-017-2.

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Abstract Let G be the F-rational points of the symplectic group Sp2n, where F is a non-Archimedean local field of characteristic 0. Cogdell, Kim, Piatetski-Shapiro, and Shahidi constructed local Lang- lands functorial lifting from irreducible generic representations of G to irreducible representations of GL2n+1(F). Jiang and Soudry constructed the descent map from irreducible supercuspidal repre- sentations of GL2n+1(F) to those of G, showing that the local Langlands functorial lifting from the irreducible supercuspidal generic representations is surjective. In this paper, based on above results, using the same descent method of studying SO2n+1 as Jiang and Soudry, we will show the rest of local Langlands functorial lifting is also surjective, and for any local Langlands parameter , we construct a representation such that and ¾ have the same twisted local factors. As one application, we prove the G-case of a conjecture of Gross-Prasad and Rallis, that is, a local Langlands parameter is generic, i.e., the representation attached to is generic, if and only if the adjoint L-function of is holomorphic at s = 1. As another application, we prove for each Arthur parameter , and the corresponding local Langlands parameter , the representation attached to is generic if and only if is tempered.

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9

Szpruch, Dani. "Some irreducibility theorems of parabolic induction on the metaplectic group via the Langlands-Shahidi method." Israel Journal of Mathematics 195, no. 2 (October 11, 2012): 897–971. http://dx.doi.org/10.1007/s11856-012-0140-y.

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10

Grobner, Harald. "Regular and residual Eisenstein series and the automorphic cohomology of Sp(2,2)." Compositio Mathematica 146, no. 1 (November 23, 2009): 21–57. http://dx.doi.org/10.1112/s0010437x09004266.

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AbstractLetGbe the simple algebraic group Sp(2,2), to be defined over ℚ. It is a non-quasi-split, ℚ-rank-two inner form of the split symplectic group Sp8of rank four. The cohomology of the space of automorphic forms onGhas a natural subspace, which is spanned by classes represented by residues and derivatives of cuspidal Eisenstein series. It is called Eisenstein cohomology. In this paper we give a detailed description of the Eisenstein cohomologyHqEis(G,E) ofGin the case of regular coefficientsE. It is spanned only by holomorphic Eisenstein series. For non-regular coefficientsEwe really have to detect the poles of our Eisenstein series. SinceGis not quasi-split, we are out of the scope of the so-called ‘Langlands–Shahidi method’ (cf. F. Shahidi,On certainL-functions, Amer. J. Math.103(1981), 297–355; F. Shahidi,On the Ramanujan conjecture and finiteness of poles for certainL-functions, Ann. of Math. (2)127(1988), 547–584). We apply recent results of Grbac in order to find the double poles of Eisenstein series attached to the minimal parabolicP0ofG. Having collected this information, we determine the square-integrable Eisenstein cohomology supported byP0with respect to arbitrary coefficients and prove a vanishing result. This will exemplify a general theorem we prove in this paper on the distribution of maximally residual Eisenstein cohomology classes.

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Dissertations / Theses on the topic "Langlands-Shahidi method"

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(8797034), Daniel J. Shankman. "Local Langlands Correspondence for Asai L and Epsilon Factors." Thesis, 2020.

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Let E/F be a quadratic extension of p-adic fields. The local Langlands correspondence establishes a bijection between n-dimensional Frobenius semisimple representations of the Weil-Deligne group of E and smooth, irreducible representations of GL(n, E). We reinterpret this bijection in the setting of the Weil restriction of scalars Res(GL(n), E/F), and show that the Asai L-function and epsilon factor on the analytic side match up with the expected Artin L-function and epsilon factor on the Galois side.

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2

(11186268), Razan Taha. "p-adic Measures for Reciprocals of L-functions of Totally Real Number Fields." Thesis, 2021.

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We generalize the work of Gelbart, Miller, Pantchichkine, and Shahidi on constructing p-adic measures to the case of totally real fields K. This measure is the Mellin transform of the reciprocal of the p-adic L-function which interpolates the special values at negative integers of the Hecke L-function of K. To define this measure as a distribution, we study the non-constant terms in the Fourier expansion of a particular Eisenstein series of the Hilbert modular group of K. Proving the distribution is a measure requires studying the structure of the Iwasawa algebra.

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3

(8782541), Dongming She. "Local Langlands Correpondence for the twisted exterior and symmetric square epsilon-factors of GL(N)." Thesis, 2020.

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In this paper, we prove the equality of the local arithmetic and analytic epsilon- and L-factors attached to the twisted exterior and symmetric square representations of GL(N). We will construct the twisted symmetric square local analytic gamma- and L-factor of GL(N) by applying Langlands-Shahidi method to odd GSpin groups. Then we reduce the problem to the stablity of local coefficients, and eventually prove the analytic stabitliy in this case by some analysis on the asymptotic behavior of certain partial Bessel functions.

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Book chapters on the topic "Langlands-Shahidi method"

1

Shahidi, Freydoon. "Langlands-Shahidi Method." In IAS/Park City Mathematics Series, 297–330. Providence, Rhode Island: American Mathematical Society, 2007. http://dx.doi.org/10.1090/pcms/012/06.

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2

Harder, Günter, and A. Raghuram. "Eisenstein Cohomology." In Eisenstein Cohomology for GL and the Special Values of Rankin-Selberg L-Functions, 71–83. Princeton University Press, 2019. http://dx.doi.org/10.23943/princeton/9780691197890.003.0006.

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This chapter provides the Eisenstein cohomology. It begins with the Poincaré duality and maximal isotropic subspace of boundary cohomology. Here, the chapter considers the compatibility of duality isomorphisms with the connecting homomorphism. It then states and proves the main result on rank-one Eisenstein cohomology. Thereafter, the chapter presents a theorem of Langlands: the constant term of an Eisenstein series. It draws some details from the Langlands–Shahidi method in this context. Induced representations are examined, as are standard intertwining operators. The chapter finally illustrates the Eisenstein series, the constant term of an Eisenstein series, and the holomorphy of the Eisenstein series at the point of evaluation.

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