Relevant bibliographies by topics / Langlands $L$-functions

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters

Academic literature on the topic 'Langlands $L$-functions'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Langlands $L$-functions"

1

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 (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
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Kim, Henry H. "On Local L-Functions and Normalized Intertwining Operators." Canadian Journal of Mathematics 57, no. 3 (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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Asgari, Mahdi. "Local L-Functions for Split Spinor Groups." Canadian Journal of Mathematics 54, no. 4 (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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Gao, Fan. "The Langlands-Shahidi L-Functions for Brylinski-Deligne Extensions." American Journal of Mathematics 140, no. 1 (2018): 83–137. http://dx.doi.org/10.1353/ajm.2018.0001.

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Kim, Wook. "Square Integrable Representations and the Standard Module Conjecture for General Spin Groups." Canadian Journal of Mathematics 61, no. 3 (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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Shahidi, Freydoon. "Twists of a General Class of L-Functions by Highly Ramified Characters." Canadian Mathematical Bulletin 43, no. 3 (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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7

Ngô, Bảo Châu. "Hankel transform, Langlands functoriality and functional equation of automorphic L-functions." Japanese Journal of Mathematics 15, no. 1 (2020): 121–67. http://dx.doi.org/10.1007/s11537-019-1650-8.

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Lomelí, Luis Alberto. "Rationality and holomorphy of Langlands–Shahidi L-functions over function fields." Mathematische Zeitschrift 291, no. 1-2 (2018): 711–39. http://dx.doi.org/10.1007/s00209-018-2100-7.

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Savin, Gordan, and Martin H. Weissman. "Dichotomy for generic supercuspidal representations ofG2." Compositio Mathematica 147, no. 3 (2011): 735–83. http://dx.doi.org/10.1112/s0010437x10005178.

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AbstractThe local Langlands conjectures imply that to every generic supercuspidal irreducible representation ofG2over ap-adic field, one can associate a generic supercuspidal irreducible representation of either PGSp6or PGL3. We prove this conjectural dichotomy, demonstrating a precise correspondence between certain representations ofG2and other representations of PGSp6and PGL3. This correspondence arises from theta correspondences inE6andE7, analysis of Shalika functionals, and spin L-functions. Our main result reduces the conjectural Langlands parameterization of generic supercuspidal irredu
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Kim, Henry H. "Langlands–Shahidi method and poles of automorphic L-functions III: Exceptional groups." Journal of Number Theory 128, no. 2 (2008): 354–76. http://dx.doi.org/10.1016/j.jnt.2007.06.012.

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Dissertations / Theses on the topic "Langlands $L$-functions"

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Rodrigues, Jacinto Joaquín. "(ϕ,Γ)-modules de de Rham et fonctions L p-adiques". Thesis, Paris 6, 2016. http://www.theses.fr/2016PA066512.

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Nous étudions, dans cette thèse, la construction des fonctions L p-adiques des motifs sur Q et, plus particulièrement, des formes modulaires. Dans les premiers trois chapitres on étend des constructions de Perrin-Riou pour construire, pour une représentation p-adique de de Rham V du groupe de Galois absolu G_Qp de Qp (ou, plus généralement, un (ϕ,Γ)-module de de Rham sur l'anneau de Robba) et un système compatible d'éléments globaux, une fonction L p-adique. On montre, en utilisant des lois de réciprocité montrées par Perrin-Riou, Colmez, Cherbonnier-Colmez, Berger et Nakamura, que ces fonctio
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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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(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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Rodrigues, Jacinto Joaquín. "Alpha Gamma-modules de de Rham et fonctions L p-adiques." Thesis, 2016. http://www.theses.fr/2016PA066512/document.

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Nous étudions, dans cette thèse, la construction des fonctions L p-adiques des motifs sur $\Q$ et, plus particulièrement, des formes modulaires.Dans les premiers trois chapitres on étend des constructions de Perrin-Riou pour construire, pour une représentation p-adique de de Rham $V$ du groupe de Galois absolu $\mathscr{G}_\qp$ de $\qp$ (ou, plus généralement, un alpha gamma-module de de Rham sur l'anneau de Robba) et un système compatible d'éléments globaux, une fonction L p-adique. On montre, en utilisant des lois de réciprocité montrées par Perrin-Riou, Colmez, Cherbonnier-Colmez, Berger et
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(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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Books on the topic "Langlands $L$-functions"

1

On certain L-functions: Conference in honor of Freydoon Shahidi on certain L-functions, Purdue Univrsity, West Lafayette, Indiana, July 23-27, 2007. American Mathematical Society, 2011.

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2

1953-, Campillo Antonio, ed. Zeta functions in algebra and geometry: Second International Workshop on Zeta Functions in Algebra and Geometry, May 3-7, 2010, Universitat de Les Illes Balears, Palma de Mallorca, Spain. American Mathematical Society, 2012.

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3

The endoscopic classification of representations orthogonal and symplectic groups. American Mathematical Society, 2013.

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4

(Contributor), S. S. Kudla, E. Kowalski (Contributor), E. de Shalit (Contributor), et al., eds. An Introduction to the Langlands Program. Birkhäuser Boston, 2003.

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5

Raghuram, Anantharam, and Günter Harder. Eisenstein Cohomology for GL and the Special Values of Rankin-Selberg L-Functions. Princeton University Press, 2019. http://dx.doi.org/10.23943/princeton/9780691197890.001.0001.

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This book studies the cohomology of locally symmetric spaces for GL(N) where the cohomology groups are with coefficients in a local system attached to a finite-dimensional algebraic representation of GL(N). The image of the global cohomology in the cohomology of the Borel–Serre boundary is called Eisenstein cohomology, since at a transcendental level the cohomology classes may be described in terms of Eisenstein series and induced representations. However, because the groups are sheaf-theoretically defined, one can control their rationality and even integrality properties. A celebrated theorem
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6

The Local Langlands Conjecture for GL(2) (Grundlehren der mathematischen Wissenschaften). Springer, 2006.

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7

Wüstholz, Gisbert, and Clemens Fuchs, eds. Arithmetic and Geometry. Princeton University Press, 2019. http://dx.doi.org/10.23943/princeton/9780691193779.001.0001.

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This book presents highlights of recent work in arithmetic algebraic geometry by some of the world's leading mathematicians. Together, these 2016 lectures—which were delivered in celebration of the tenth anniversary of the annual summer workshops in Alpbach, Austria—provide an introduction to high-level research on three topics: Shimura varieties, hyperelliptic continued fractions and generalized Jacobians, and Faltings heights and L-functions. The book consists of notes, written by young researchers, on three sets of lectures or minicourses given at Alpbach. The first course contains recent r
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Book chapters on the topic "Langlands $L$-functions"

1

de Shalit, Ehud. "Artin L Functions." In An Introduction to the Langlands Program. Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-0-8176-8226-2_4.

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2

Kowalski, E. "Elementary Theory of L-Functions I." In An Introduction to the Langlands Program. Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-0-8176-8226-2_1.

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Kowalski, E. "Elementary Theory of L-Functions II." In An Introduction to the Langlands Program. Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-0-8176-8226-2_2.

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de Shalit, Ehud. "L-Functions of Elliptic Curves and Modular Forms." In An Introduction to the Langlands Program. Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-0-8176-8226-2_5.

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Cogdell, J. W. "Analytic Theory of L-Functions for GL n." In An Introduction to the Langlands Program. Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-0-8176-8226-2_9.

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Shahidi, Freydoon. "Automorphic L-Functions." In The Genesis of the Langlands Program. Cambridge University Press, 2021. http://dx.doi.org/10.1017/9781108591218.020.

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Goldfeld, Dorian, and Hervé Jacquet. "Automorphic Representations and L-Functions for GL(n)." In The Genesis of the Langlands Program. Cambridge University Press, 2021. http://dx.doi.org/10.1017/9781108591218.019.

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Emerton, Matthew. "Langlands Reciprocity: L-Functions, Automorphic Forms, and Diophantine Equations." In The Genesis of the Langlands Program. Cambridge University Press, 2021. http://dx.doi.org/10.1017/9781108591218.021.

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IBUKIYAMA, T. "Siegel Modular Forms of Weight Three and Conjectural Correspondence of Shimura Type and Langlands Type." In The Conference on L-Functions. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812772398_0003.

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10

Harder, Günter, and A. Raghuram. "Eisenstein Cohomology." In Eisenstein Cohomology for GL and the Special Values of Rankin-Selberg L-Functions. 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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