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Topic: Automorphic form

	Introduction to social network methods: Chapter 14: Automorphic equivalence
		Automorphic equivalence is not as demanding a definition of similarity as structural equivalence, but is more demanding than regular equivalence.
		Automorphic equivalence begins to change the focus of our attention, moving us away from concern with individual's network positions, and toward a more abstracted view of the network.
		Automorphic equivalence asks if the whole network can be re-arranged, putting different actors at different nodes, but leaving the relational structure or skeleton of the network intact.
	faculty.ucr.edu /~hanneman/nettext/C14_Automorphic_Equivalence.html (2581 words)

	Robert Langlands - Wikipedia, the free encyclopedia
		During the early 1960s he developed the general theory of Eisenstein series for discrete groups, initiated by Atle Selberg; this, roughly speaking, is the continuous spectrum theory of automorphic forms, for arithmetic groups in semisimple groups.
		Langlands understood that the theory of automorphic representation offers a generalization of class field theory, a central topic in algebraic number theory.
		Using every tool at their disposal, they gave a surprisingly complete theory of automorphic forms on the general linear group GL(2), establishing important cases of functoriality.
	en.wikipedia.org /wiki/Robert_langlands (435 words)

	Springer Online Reference Works
		The study of modular functions began in the 19th century in connection with the study of elliptic functions and preceded the appearance of the general theory of automorphic functions.
		corresponds to a period parallelogram in the form of a rhombus with angles
		The modular group (1) is then replaced by the modular group of automorphisms of the unit disc.
	eom.springer.de /m/m064430.htm (682 words)

	Automorphic Forms on SL2 (R) - Cambridge University Press
		Automorphic Forms on SL2 (R) Series: Cambridge Tracts in Mathematics (No. 130)
		This book provides an introduction to some aspects of the analytic theory of automorphic forms on G=SL2(R) or the upper-half plane X, with respect to a discrete subgroup G of G of finite covolume.
		Finite dimensionality of the space of automorphic forms of a given type; 9.
	www.cambridge.org /uk/catalogue/catalogue.asp?isbn=0521580498 (259 words)

	RANKIN-SELBERG WITHOUT UNFOLDING AND BOUNDS ON SPHERICAL FOURIER COEFFICIENTS OF MAASS FORMS (Site not responding. Last check: 2007-11-01)
		The sum formula of Kuznetsov is a relation between Kloosterman sums and Fourier coefficients and automorphic forms.
		The formula is related to a recent conjecture of Sarnak regarding the L-infinity norm of automorphic forms on symmetric spaces.
		The proofs of the new bounds utilise the spectral theory of automorphic functions (especially certain ideas of Deshouillers and Iwaniec and a bound of Kim and Sarnak for the eigenvalues of Hecke operators).
	www.math.technion.ac.il /cms/art_to_ant/abstracts.htm (885 words)

	[No title]
		To be precise: if we form the function pi^{-s/2} Gamma(s/2) zeta(s) then this function is unchanged by the transformation s -> 1 - s This symmetry maps the line Re(s) = 1/2 to itself, and the Riemann Hypothesis says all the zeta zeros in the critical strip actually lie on this magic line.
		The Dirichlet characters give automorphic forms, but automorphic forms are a vector space so you can add them together and get an automorphic form for any periodic function.
		Let K be a number field and assume K is Galois over Q (equivalently, that there is a polynomial f with rational coefficients such that K is the smallest subfield of the complex numbers containing all the roots of f; K is called the "splitting field" of f).
	math.ucr.edu /home/baez/twf_ascii/week217 (4253 words)

	A bounded automorphic form of dimension zero is constant, M. I. Knopp, J. Lehner, M. Newman
		A bounded automorphic form of dimension zero is constant, M. Knopp, J. Lehner, M. Newman
		A bounded automorphic form of dimension zero is constant
		A subscription is required to access articles in the Duke Mathematical Journal (2000-) and in DMJ 100 (1935-1999).
	projecteuclid.org /getRecord?id=euclid.dmj/1077375917 (96 words)

	Robert Langlands' work
		It is this confirmation of functoriality in its relation to the Artin conjecture and the introduction of the local correspondence that is, in my view, one of the two principal contributions of Jacquet-Langlands to a clearer, more mature formulation of functoriality and to a more solidly based confidence in its validity.
		In that letter the suggestions were entirely global, whereas in the published lecture Problems in the theory of automorphic forms the global conjectures had local counterparts.
		One project that was formulated after writing the letter to Weil and that was suggested by his 1957 paper on the Hecke theory was to establish a representation-theoretic form of it and to acquire thereby a clearer notion of the implications of the conjectures.
	www.sunsite.ubc.ca /DigitalMathArchive/Langlands/JL.html (1844 words)

	Amazon.com: Automorphic Forms on SL2 (R) (Cambridge Tracts in Mathematics): Books: Armand Borel (Site not responding. Last check: 2007-11-01)
		This book provides an introduction to some aspects of the analytic theory of automorphic forms on G=SL2(R) or the upper-half plane X, with respect to a discrete subgroup ^D*G of G of finite covolume.
		Elementary theory of Lie groups and Lie algebras, and the interpretation of the elements of the Lie algebra as differential operators on the group or its coset spaces.
		Please note that we are unable to respond directly to all feedback submitted via this form, but we'll ask you to sign in so we can contact you if needed.
	www.amazon.com /exec/obidos/tg/detail/-/0521580498?v=glance (641 words)

	Fields Institute - Automorphic Forms
		The theory of automorphic forms is a wide and deep subject touching many areas of mathematics.
		An important problem is to express the Hasse-Weil zeta function of a Shimura variety in terms of automorphic L-functions.
		Here in order to define the local factors not just at primes of good reduction, we need to study the variety at the finite set of primes of bad reduction.
	www.fields.utoronto.ca /programs/scientific/02-03/automorphic_forms (423 words)

	[No title] (Site not responding. Last check: 2007-11-01)
		I will review the classical examples of spherical functions and generalizations thereof, which are important in the study of automorphic forms.
		In the theory of automorphic forms, spherical functions are one of several ingredients in the local theory.
		As an application we will discuss a higher rank analogue of a result of Waldspurger that relates a sum of an automorphic form over CM-points to a special value of an L-function at the center of symmetry.
	www.math.technion.ac.il /~techm/20060309160020060309off (134 words)

	The inner product of an automorphic wave form with the pullback of an Eisenstein series, Shinji Niwa
		[8] H. Yoshida, Sieges modular forms and the arithmetic of quadratic forms, Invent.
		[9] H. Yoshida, On an explicit construction of Siegel modular forms of genus 2, Proc.
		[13] P. Garrett, Pullbacks of Eisenstein series, in Automorphic forms in several variables (Proceedings of a Taniguchi symposium), Birkhauser, 1984.
	projecteuclid.org /getRecord?id=euclid.nmj/1118780830 (317 words)

	Citebase - An automorphic form related to cubic surfaces (Site not responding. Last check: 2007-11-01)
		Citebase - An automorphic form related to cubic surfaces
		Authors: Borcherds, R. This is a note constructing a certain weight 4 automorphic form on the moduli space of cubic surfaces, posted here because it is referred to in math.AG/0002066
		Users are cautioned not to use it for academic evaluation yet.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/0002079 (92 words)

	AMCA: Genuine representations of the metaplectic group by David Renard (Site not responding. Last check: 2007-11-01)
		One example is the Langlands-Shelstad theory of stable conjugacy and endoscopic transfer, which has its root in automorphic form theory.
		Another example is Vogan's Kazhdan-Lusztig algorithm to compute characters of irreducible admissible representations of such groups, and Vogan's duality of characters.
		On the other hand, non-linear groups, specially the metaplectic group, appear in dual pairs correspondences which play an important role in automorphic form theory.
	at.yorku.ca /c/a/e/x/45.htm (159 words)

	week217
		I still need to say more about which puzzles give automorphic forms, what it really means when they do.
		These p functions on Z form a basis of the vector space of periodic functions on Z with period p.
		, the dihedral group with 8 elements (the four roots form a square in the complex plane and it's the symmetries of this square).
	math.ucr.edu /home/baez/week217.html (4450 words)

	This Week's Finds in Mathematical Physics (Week 217)
		So, please either reread "week197" or take my\nword for it: modular forms are cool!\n\nThe theta function is almost a modular form, but not quite.
		The fact that they satisfy a "functional\nequation" is just another way of saying their Mellin transforms are\nautomorphic forms...
		function is almost a modular form, but not quite.
	www.physicsforums.com /showthread.php?t=77435 (4735 words)

	DISTRIBUTION THEOREMS OF L-FUNCTIONS (Site not responding. Last check: 2007-11-01)
		Chapter 7: Prime number theorems for automorphic l-adic motives
		1.5 Automorphic l-adic motives in characteristic p>0 (a sketch)
		This book is an attempt to extend some of Montgomery's and Selberg's techniques to more general types of L-functions.
	www.nadn.navy.mil /MathDept/wdj/numbook.html (210 words)

	Publisher description for Library of Congress control number 97006027
		Publisher description for Automorphic forms on SL(R) / Armand Borel.
		Graduate students and researchers in analytic number theory will find much to interest them in this book.
		Library of Congress subject headings for this publication: Automorphic forms
	www.loc.gov /catdir/description/cam028/97006027.html (154 words)

	This Week's Finds in Mathematical Physics (Week 217) Text - Physics Forums Library
		I also explained how modular forms are related to elliptic\ncurves and string theory.
		Indeed, it doesn't change at all when we add 2 to t, since \exp(2 \pi i) = 1.
		I also explained how modular forms are related to elliptic
	www.physicsforums.com /archive/index.php/t-77435.html (4095 words)

	Automorphic Forms and Number Theory Seminar
		Multiplicity-One theorem for generic cuspidal automorphic representations of GSp(4) [conclusion]
		The Multiplicity One Theorem for generic cuspidal automorphic forms of GSp(4)
		On Maass lifts and the central critical values of triple product L-functions.
	www.math.umn.edu /~garrett/seminar (423 words)

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