
	Where results make sense

Topic: Automorphic cuspidal representation

In the News (Thu 31 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Langlands program - Wikipedia, the free encyclopedia
		The Artin reciprocity law applies to an algebraic number field whose Galois group over Q is abelian, assigns L-functions to the one-dimensional representations of this Galois group; and states that these L-functions are identical to certain Dirichlet L-series (that is, the analogues of the Riemann zeta function constructed from Dirichlet characters).
		Langlands attached L-functions to these automorphic representations, and conjectured that every L-function arising from finite-dimensional representations of the Galois group is equal to one arising from an automorphic cuspidal representation.
		It is of the nature of an induced representation construction — what in the more traditional theory of automorphic forms had been called a 'lifting', known in special cases, and so is covariant (where a restricted representation is contravariant).
	en.wikipedia.org /wiki/Langlands_program (844 words)

	[No title]
		$L(\xi \nu, \nu ^{-1/2}\pi _{2}))$ of the induced representation $\xi \nu \rtimes \nu ^{-1/2}\pi _{2}$ of $H$, where $\pi _{2}$ is a cuspidal $($irreducible$)$ representation of $\GL (2,F)$ with central character $\xi \neq 1=\xi ^{2}$ and $\xi \pi _{2}=\pi _{2}$, $\lambda $-lifts to the square integrable $($resp.
		The [quasi-]packet $\{\pi _{H}\}$ of an automorphic representation $\pi _{H}$ is defined by the local [quasi-]packets $\{\pi _{Hv}\}$ of the components $\pi _{Hv}$ of $\pi _{H}$ at almost all places.
		A discrete spectrum representation $\pi _{H}$ with component $L(\nu _{v}\xi _{v}, \nu _{v}^{-1/2}\pi _{2v})$ (whose packet consists of itself), where $\pi _{2v}$ is a cuspidal representation with central character $\xi _{v}\neq 1=\xi _{v}^{2}$ and $\xi _{v}\pi _{2v}=\pi _{2v}$, is in the packet of $L(\nu \xi,\nu ^{-1/2}\pi _{2})$.
	www.emis.de /journals/ERA-AMS/2004-01-005/2004-01-005.tex.html (4854 words)

	Automorphic form (Site not responding. Last check: 2007-11-05)
		In mathematics, the general notion of automorphic form is the extension to analytic functions, perhaps of several complex variables, of the theory of modular forms.
		The subsequent notion of automorphic representation has proved of great technical value for dealing with G an algebraic group, treated as an adelic algebraic group.
		Under Poincaré's definition, an automorphic function is a function where which is analytic under its domain and which is invariant under a denumerable infinite group of linear fractional transformations; they are the generalizations of trigonometric functions and elliptic functions.
	www.worldhistory.com /wiki/A/Automorphic-form.htm (1030 words)

	Automorphic Representations of the Jacobi group and of GL 2 - Schmidt (ResearchIndex) (Site not responding. Last check: 2007-11-05)
		Automorphic Representations of the Jacobi group and of GL 2 (1998)
		Abstract: A lifting map from cuspidal automorphic representations of the Jacobi group G J to cuspidal automorphic representations of the group PGL(2) is constructed.
		The main idea in the construction is to exploit the close relationship between representations of G J and of the metaplectic group Mp, and then to make use...
	citeseer.ist.psu.edu /schmidt98automorphic.html (555 words)

	Summer Seminar
		Abstract: An automorphic representation of the metaplectic cover of GL is called "distinguished" if it has a unique Whittaker model.
		In 1984, Patterson and Piatetski-Shapiro constructed cuspidal distinguished representations on the three-fold covers of GL(3) using the method of the converse theorem.
		These locally analytic representations are expected to be the p-adic local factors in certain global objects which are obtained by p-adically interpolating modular forms.
	www.math.wisc.edu /~thyang/Spring04.html (988 words)

	Fields Institute - Program on Automorphic Forms - Course Information (Site not responding. Last check: 2007-11-05)
		The theory of L-functions of automorphic forms (or modular forms) via integral representations has its origin in the paper of Riemann on the zeta-function.
		L-functions of automorphic representations were first developed by Jacquet and Langlands for GL(2).
		In the context of automorphic representations, the Converse Theorem for GL(2) was developed by Jacquet and Langlands, extended and significantly strengthened to GL(3) by Jacquet, Piatetski-Shapiro, and Shalika, and then extended to GL(n).
	www.fields.utoronto.ca /programs/scientific/02-03/automorphic_forms/courses (875 words)

	Nadya Gurevich's talk (Site not responding. Last check: 2007-11-05)
		Given a cuspidal representation of a symplectic group the theta correspondence method returns an automorphic representation of an orthogonal group.
		It is possible to decide whether the image is cuspidal by considering a tower of theta correspondences.
		To determine the first place when the image of a given representation is nonzero is the fundamental problem of the theta correspondence method.
	www.math.tau.ac.il /~borovoi/sem/nadya2005.html (107 words)

	Journal of Lie Theory, 7(2), 201-229 (1997) (Site not responding. Last check: 2007-11-05)
		Abstract: In this article, one studies the theta correspondance between automorphic representations of an even orthogonal group and a symplectic group.
		Fix an irreducible cuspidal representation, $\pi$, of the othogonal group.
		One gives also an answer for the symetric question, $\pi$ is now a representation of the symplectic group; here one allows change of the orthogonal space saving the dimension.
	www.mat.ub.es /EMIS/journals/JLT/vol.7_no.2/moeg1pl.html (113 words)

	Annals of Mathematics, II. Series, Vol. 150, No. 3, pp. 807-866, 1999
		Let \$\sigma\$ be an automorphic representation of either a split special orthogonal group \$SO_r({\Bbb A})\$ or a symplectic group \$Sp_{2k}({\Bbb A})\$.
		Then the Langlands functoriality conjecture predicts the existence of an automorphic representation \$\pi(\sigma)\$ on a suitable general linear group \$GL_m({\Bbb A})\$.
		Conversely, given \$\pi\$ on \$GL_m({\Bbb A})\$, self-dual and cuspidal, then from the factorization of the partial Rankin-Selberg convolution of \$\pi\$ with itself \$L^S(s,\pi\otimes \pi)=L^S(s,\pi,\wedge^2)L^S(s,\pi,\vee^2)\$ and the pole of the left-hand side at \$s=1\$, one expects that \$\pi\$ is the \`\`backwards lift" of some \$\sigma(\pi)\$ on an orthogonal or symplectic group.
	www.math.helsinki.fi /EMIS/journals/Annals/150_3/3.html (518 words)

	A non-selfdual automorphic representation of ... and a Galois representation (ResearchIndex) (Site not responding. Last check: 2007-11-05)
		Abstract: The Langlands philosophy contemplates the relation between automorphic representations and Galois representations.
		A particularly interesting case is that of the non-selfdual automorphic representations of GL 3.
		Clozel conjectured that the L-functions of certain of these are equal to L-functions of Galois representations.
	citeseer.ifi.unizh.ch /491980.html (218 words)

	Cusp Forms on GL(2n) with GL(n) × GL(n) PERIODS, AND SIMPLE ALGEBRAS (ResearchIndex) (Site not responding. Last check: 2007-11-05)
		For D \Theta = GL(1), the period is the value at 1=2 of the L-function of the cusp form on GL(2; A).
		A cuspidal representation is called cyclic if it contains a cusp form with a non zero period.
		4 function attached to a cuspidal automorphic representation o..
	citeseer.ist.psu.edu /flicker96cusp.html (476 words)

	Number Theory Seminars in JHU (Site not responding. Last check: 2007-11-05)
		Selberg's orthogonality conjecture predicts that the coefficients of automorphic L-functions attached to different cuspidal representations are orthogonal.
		In particular, an L-function attached to a cuspidal representation of GL(m) over Q cannot be factored further.
		Our results can be used to characterize asymptotically whether two cuspidal representations are equivalent, twisted equivalent, or not twisted equivalent at all.
	www.math.jhu.edu /~qzhang/Seminar/Seminar-2003Fall.htm (937 words)

	Citations: the Ramanujan conjecture and the finiteness of poles for certain L-functions - Shahidi (ResearchIndex) (Site not responding. Last check: 2007-11-05)
		For r = 3, one also knows, by the work of Bump, Ginzburg and Ho#stein, that the (symmetric cube) L function is holomorphic in #(s) # 3 4 ; but we will not have occasion to use this.
		Modularity of Solvable Artin Representations of GO(4)-Type - Ramakrishnan
		....representation of GL(n; A F) with coefficients a(P) a P (Fix t 0: Then the set of primes P such that ja(P)j N(P) t has density zero.
	citeseer.ifi.unizh.ch /context/1824916/0 (1023 words)

	Schneider, Stuhler: Representation theory and sheaves on the Bruhat-Tits building
		Representation theory and sheaves on the Bruhat-Tits building.
		KATO, Duality for representations of a Hecke algebra, Proc.
		STUHLER, Resolutions for smooth representations of the general linear group over a local field, J. reine angew.
	www-mathdoc.ujf-grenoble.fr /numdam-bin/item?id=PMIHES_1997__85__97_0 (471 words)

	Langlands program - free-definition (Site not responding. Last check: 2007-11-05)
		The starting point of the program is the Artin reciprocity law which generalizes quadratic reciprocity.
		Langlands then generalized these to automorphic cuspidal representations, which are certain infinite dimensional irreducible representations of the general linear group over the adele ring of Q.
		Langlands then formulated a much more general "Functoriality Principle", which relates automorphic representations of different groups (not just the general linear group) over the adele ring of Q, in a way which is compatible with their L-functions.
	www.free-definition.com /Langlands-program.html (680 words)

	Fields Institute - Workshop on Automorphic L-functions
		It will be shown that they are automorphic and square integrable and have many vanishing Fourier coefficients which allow them to be used as theta kernels and potentially in the Rankin-Selberg method.
		Supposedly, one of the consequences of functoriality is the ability to then ``pull back'' various structural facts about automorphic representations of GL(N) to these groups.
		To a representation $\pi$ of ${\rm SL}_2(F)$ we attach an integer $c(\pi)$ that we call the conductor of $\pi$.
	www.fields.utoronto.ca /programs/scientific/02-03/automorphic_forms/L-functions/abstracts.html (1029 words)

	AMS Online Books/pspum31
		Representations of reductive Lie groups by N.R. Wallach
		Representations of {german p}-adic groups: A survey by P. Cartier
		Automorphic forms and automorphic....by A. Borel and H. Jacquet
	www.ams.org /online_bks/pspum331 (98 words)

	Ginzburg, Rallis, Soudry: $L$-functions for symplectic groups
		— Exterior square L-functions, in Automorphic forms, Shimura varieties and L-functions, L. Clozel and J. Milne eds, vol.
		[P] Representations de Schrödinger, Indice de Maslov et groupe metaplectique, in Non Commutative Harmonic Analysis and Lie Groups, Proc.
		— Lie groups representations and harmonic polynomials of a matrix variable, Trans.
	www.numdam.org /numdam-bin/item?id=BSMF_1998__126_2_181_0 (236 words)

	[No title]
		\newblock {\em Automorphic forms and representations}, volume~55 of {\em Cambridge Studies in Advanced Mathematics}.
		\newblock {A Rankin-Selberg integral for the adjoint representation of $GL_3$}.
		\newblock {The symmetric-square L-function attached to a cuspidal automorphic representation of $GL_3$}.
	sporadic.stanford.edu /bump/rallis/rallis.bbl (858 words)

	HKUST Institutional Repository: Item 1783.1/1970 (Site not responding. Last check: 2007-11-05)
		An integral representation of automorphic L-function for quasi-split unitary groups
		This gives an integral representation of the standard Langlands L-function of a cuspidal automorphic representation of the group U (n, n), attached to a 4n dimensional representation of its L-group.
		Our method is parallel to that of Piatetski-Shapiro and Rallis, who dealt with the case of symplectic groups.
	hdl.handle.net /1783.1/1970 (109 words)

	Gelbart, Jacquet: A relation between automorphic representations of ${\rm GL}(2)$ and ${\rm GL}(3)$
		Gelbart, Jacquet: A relation between automorphic representations of ${\rm GL}(2)$ and ${\rm GL}(3)$
		A relation between automorphic representations of ${\rm GL}(2)$ and ${\rm GL}(3)$.
		LANGLANDS, On the Notion of an Automorphic Rrepresentation [Proc.
	www.numdam.org /numdam-bin/item?id=ASENS_1978_4_11_4_471_0 (302 words)

	Rohlfs, Speh: Automorphic representations and Lefschetz numbers
		CLOZEL, On the Cuspidal Cohomology of Arithmetic Subgroups of SL (2n) and the First Betti Number of Arithmetic 3-Manifolds (Duke.
		SPEH, Representations with Cohomology in the Discrete Spectrum of Subgroups of SO (n, 1) (ℤ) and Lefschetz Numbers, (Ann.
		SPEH, Unitary Representations of Gl (n, ℝ) with Non-Trivial (g, ŧ)-Cohomology (Invent.
	www-mathdoc.ujf-grenoble.fr /numdam-bin/item?id=ASENS_1989_4_22_3_473_0 (444 words)

	Bulletin of the American Mathematical Society
		-functions and their analytic properties have assumed a central role in number theory and automorphic forms.
		Jian-Shu Li and Joachim Schwermer, Automorphic representations and cohomology of arithmetic groups, Challenges for the 21st century (Singapore, 2000), World Sci.
		Jonathan D. Rogawski, Automorphic representations of unitary groups in three variables, Annals of Mathematics Studies, vol.
	www.ams.org /bull/2004-41-01/S0273-0979-03-00995-9/home.html (2686 words)

	DC MetaData for: On zeroes of automorphic L-functions (Site not responding. Last check: 2007-11-05)
		DC MetaData for: On zeroes of automorphic L-functions
		cuspidal automorphic representation of the units in such
		Keywords: simple algebras, general linear groups, cuspidal automorphic representations, zeroes of L-functions
	www.esi.ac.at /Preprint-shadows/soule.html (104 words)

	Arizona Mathematics \| Events \| Weekly News \| Spring 2003 \| February 17 - February 21, 2003 (Site not responding. Last check: 2007-11-05)
		Cetin Urtis, Department of Mathematics, University of Arizona, will speak on “Integral Representations of L-functions by the Doubling Method", at 2:00 PM in MATH 402.
		Abstract: We will give explicit constructions of standard L-functions by the "doubling method" which was introduced by Piatetski-Shapiro and Rallis in 1987.
		This is a generalization of the classical Rankin-Selberg construction to define an L-function associated to any irreducible cuspidal automorphic representation.
	math.arizona.edu /~weeklynews/spring2003/2003_02_17.html (1147 words)

	Langlands program - Encyclopedia Glossary Meaning Explanation Langlands program (Site not responding. Last check: 2007-11-05)
		If you find this encyclopedia or its sister projects useful,
		Artin's law applies to an algebraic number field whose Galois group over Q is abelian, assigns L-functions to the one-dimensional representations of this Galois group; and states that these L-functions are identical to certain Dirichlet L-series (that is, the analogues of the Riemann Zeta function constructed from Dirichlet characters).
		Erich Hecke had earlier related Dirichlet L-functions with automorphic forms (holomorphic functions on the upper half place of C that satisfy certain functional equations).
	www.encyclopedia-glossary.com /en/Langlands-program.html (887 words)

	Dipartimento di Matematica - Università di Torino (Site not responding. Last check: 2007-11-05)
		Let f be a newform with respect to the multiplicative group
		be the automorphic cuspidal representation defined by f.
		Fix a quadratic imaginary subfield K of D.
	www.dm.unito.it /quadernidipartimento/quaderni.php?action=view_abs&article=q20-99.htm (169 words)

	Citebase - On the exceptional zeros of Rankin-Selberg L-functions (Site not responding. Last check: 2007-11-05)
		[La79]: R.P. Langlands, On the notion of an automorphic representation.
		A supplement, in Automorphic forms, Representations and L-functions, ed.
		(PPS89):S. Patterson and I. Piatetski-Shapiro, The symmetric-square L function attached to a cuspidal automorphic representation of GL 3, Math.
	citebase.eprints.org /cgi-bin/citations?archiveID=oai:arXiv.org:math/0108054 (933 words)

	[No title]
		Math.", year = 1998, volume = 120, pages = "723--755" } @Article{PattersonPSSymmetric, author = "S. Patterson and I. Piatetski-Shapiro", title = "{The symmetric-square L-function attached to a cuspidal automorphic representation of $GL_3$}", journal = "Math.
		Proc." } @InProceedings{JacquetShalikaExterior, author = "H. Jacquet and J. Shalika", title = "{Exterior square $L$-functions}", booktitle = "Automorphic forms, Shimura varieties, and $L$-functions, Vol.
		Ann.}, year = 1977, volume = 226, pages = {81--94} } @InProceedings{GarrettFactorization, author = {P. Garrett}, title = "{Euler factorization of global integrals}", booktitle = "{Automorphic forms, automorphic representations, and arithmetic (Fort Worth, TX, 1996), Part 2}", pages = {35--101}, year = 1999, volume = 66, series = {Proc.
	sporadic.stanford.edu /bump/rallis/rallis.bib (1825 words)

Try your search on: Qwika (all wikis)