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Topic: Automorphic number

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	tingilinde: take a number ...
		22 is the number of partitions of 8.
		101 is the number of partitions of 13.
		231 is the number of partitions of 16.
	tingilinde.typepad.com /starstuff/2005/11/significant_int.html (12385 words)

	What's special about this number? (3)
		is the number of planar partitions of 12.
		is the number of degrees in a circle.
		is the number of planar partitions of 13.
	www.archimedes-lab.org /numbers/Num201_500.html (1994 words)

	What's Special About This Number?
		is the number of planar partitions of 10.
		is the number of planar partitions of 11.
		is the number of planar partitions of 14.
	www.stetson.edu /~efriedma/numbers.html (7410 words)

	Upto11.net - Wikipedia Article for 6 (number) (Site not responding. Last check: 2007-11-07)
		Six is the second smallest composite number, its proper divisors being 1, 2 and 3.
		The number of feet below ground level a coffin is traditionally buried; thus, the phrase "six feet under" means that a person (or thing, or concept) is dead.
		The number of similar coins that can be arranged around a central seventh coin of the same kind so that each coin makes contact with the central one and touches both its neighbors without a gap; see also Sphere packing.
	www.upto11.net /generic_wiki.php?q=6 (1040 words)

	5.2.4 Number Theory
		The number theory group at Oklahoma State University has established a thriving program of research, including a regular seminar series featuring lectures of both a research and expository nature by the resident number theorists, as well as frequent lectures by distinguished young and senior number theorists from around the country.
		Number theory is famed not just for the beauty of its theorems, but for the enormous wealth and variety of techniques involved in discovering and proving these theorems.
		Our faculty is prepared to offer courses in algebraic number theory, class field theory, analytic number theory, the arithmetic of elliptic curves as well as other arithmetic algebraic varieties, p-adic analysis, automorphic and modular forms, discrete subgroups of algebraic groups, computational number theory, as well as many other subfields of number theory.
	www.math.okstate.edu /~graddir/long-hbk/5_2_4Number_Theory.html (395 words)

	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 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.
		Having selected a number of partitions, it is useful to re-run the algorithm a number of times to insure that a global, rather than local minimum has been found.
	faculty.ucr.edu /~hanneman/nettext/C14_Automorphic_Equivalence.html (2581 words)

	Automorphic Numbers
		One of the topic of the recreational mathematics is the Automorphic numbers which have many use in different fields.
		By definition 0 is not an Automorphic Number and for this particular problem we will not consider 1 as an Automorphic Number.
		In this problem you are to determine whether a given number is Automorphic or not.
	acm.uva.es /p/v104/10433.html (173 words)

	Square number - Wikipedia, the free encyclopedia
		In mathematics, a square number, sometimes also called a perfect square, is an integer that can be written as the square of some other integer.
		The sum of two consecutive square numbers is a centered square number.
		If the last digit of a number is 0, its square ends in 00 and the preceding digits must also form a square.
	en.wikipedia.org /wiki/Square_number (770 words)

	Automorphic number - Wikipedia, the free encyclopedia
		In mathematics an automorphic number (sometimes referred to as a circular number) is a number whose square "ends" in the number itself.
		The automorphic numbers begin 1, 5, 6, 25, 76, 376, 625, 9376,...
		There are at most two automorphic numbers with k digits, one ending in 5 and one ending in 6 (unless k = 1, when there are three).
	en.wikipedia.org /wiki/Automorphic_number (137 words)

	Wikinfo \| Square number (Site not responding. Last check: 2007-11-07)
		In mathematics, a square number, sometimes also called a perfect square, is a positive integer that can be written as the square of some other integer.
		So for example, 9 is a square number since it can be written as 3×3.
		A square number is also the sum of two consecutive triangular numbers.
	www.wikinfo.org /wiki.php?title=Square_number (345 words)

	MATHEWS: Automorphic Numbers (Site not responding. Last check: 2007-11-07)
		The first automorphic numbers are (Sloane's A003226) 1, 5, 6, 25, 76, 376, 625, 9376,...
		Defined as automorphic numbers except that the square is replaced by the cube of the number.
		The first trimorphic numbers are (Sloane's A033819) 1, 4, 5, 6, 9, 24, 25, 49, 51, 75, 76, 99, 125, 249, 251, 375, 376,...
	www.wschnei.de /digit-related-numbers/automorphic-numbers.html (285 words)

	Nick's Mathematical Puzzles: Solution 94
		Numbers are written in standard decimal notation, with no leading zeroes.
		Since n is a 2-digit number, neither n nor n − 1 is divisible by 100.
		Hence there is always precisely one automorphic number ending in 5, and one ending in 6, subject to the caveat that each number may have one or more leading zeroes.
	www.qbyte.org /puzzles/p094s.html (265 words)

	What's special about this number? (2) (Site not responding. Last check: 2007-11-07)
		is a Pell number and the smallest abundant number that is not the sum of some subset of its divisors.
		is a 17-gonal number and a Smith number (a Smith number is a composite number the sum of whose digits is the sum of the digits of its prime factors excluding 1, here: 9 + 4 = 2 + 4 + 7).
		One of the largest numbers, that is not a power of 10, that has a specific word ('gross') assigned to it.
	www.archimedes-lab.org /numbers/Num70_200.html (2941 words)

	[No title]
		L-functions have been used for over a century in number theory; Langlands isolated the correct analogue from representation theory (so-called "automorphic" L-functions) and was the first to understand the general picture.
		As an example of why one might expect some sort of connection between Lie groups and number theory, consider the Galois group G = Gal(K/L) where K is an algebraic closure of a number field L. Number theorists are very interested in representations of K. G is a profinite group (projective limit of finite groups).
		(German) [The role of zeta functions in number theory, from Euler to the present] Ceremony and scientific conference on the occasion of the 200th anniversary of the death of Leonhard Euler (Berlin, 1983), 120--124, Abh.
	www.math.niu.edu /~rusin/known-math/94/langlands (908 words)

	Robert Langlands' work - automorphics forms
		The letter to Weil included a number of striking conjectures which eventually changed much of the direction of research in automorphic forms.
		Some of their consequences were explained in a graduate course given at Princeton in the spring of 1967, and then things were put in a somewhat wider context in a series of lectures at Yale later that Spring.
		These two observations underline that functoriality arose in an attempt to find a nonabelian class-field theory under the influence of the view, which arose in the early sixties, that much of the theory of automorphic forms could and should be treated in the context of group representations.
	www.sunsite.ubc.ca /DigitalMathArchive/Langlands/automorphic.html (829 words)

	Number Theory at Unb (Site not responding. Last check: 2007-11-07)
		Number theory, as Gauss said, is the queen of mathematics.
		Automorphic forms are a modern part with old roots in which one meets geometry, analysis, algebra and number theory in the study of groups, their representations and their harmonic analysis.
		Representation theory and automorphic forms along the lines developed by Langlands and his school, particularly the study of Heisenberg groups, Weil representation and Whittaker models for the unitary groups.
	www.mat.unb.br /~hemar/nt.html (293 words)

	Numbers
		Two numbers n and m are called an amicable pair if the sum of all positive divisors of n is equal to the sum of all positive divisors of m and both are equal to n + m.
		Pentagonal numbers are to pentagons what triangular numbers are to triangles and square numbers are to squares.
		Definition: The number n is called a weird number if it is abundant but is not the sum of any subset of its proper factors.
	www.tanyakhovanova.com /Numbers/numbers.html (2047 words)

	3.2.4 Number Theory
		Number theory has drawn on and inspired developments in complex analysis, harmonic analysis, representation theory, and algebraic geometry.
		James Cogdell: Automorphic representations and L-functions, including L-functions for automorphic representations of GL(n).
		Extension of Hecke's converse theorem to GL(n); applications of this converse theorem to liftings of automorphic forms and indirectly to class field theory.
	www.math.okstate.edu /grad/brief-hbk/3_2_4Number_Theory.html (395 words)

	Automorphic Forms on SL2 (R) - Cambridge University Press
		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.
		The point of view is inspired by the theory of infinite dimensional unitary representations of G; this is introduced in the last sections, making this connection explicit.
		Finite dimensionality of the space of automorphic forms of a given type; 9.
	www.cambridge.org /uk/catalogue/catalogue.asp?isbn=0521580498 (259 words)

	The Number Theory Group at UCLA
		UCLA has a well-established research group in Number Theory, especially in those areas where the theory of automorphic forms plays an important role.
		Additionally, a number of UCLA faculty members specialize in closely affiliated areas, such as K-theory, quadratic forms, additive combinatorics, and cryptography.
		Graduate study in number theory at UCLA is based on lecture courses, faculty-led student seminars, and individual study.
	www.math.ucla.edu /~ntg (381 words)

	Solomon Friedberg
		For a.pdf file which gives an annotated bibliography of introductory material on automorphic forms, which should be of use to graduate students considering working in the area, click here.
		Penn State University (two talks: one on number theory and on one TA development via case studies), November 2005.
		Number Theory Conference in Honor of Harold Stark, University of Minnesota, August 2004 (conference co-organizer).
	www2.bc.edu /~friedber (905 words)

	D. Prasad (Site not responding. Last check: 2007-11-07)
		In paper [40] in the conference proceedings of a conference at the Tata Institute on Automorphic forms, I elaborate on a conjecture with B. Gross which gives a very precise structure for the space of degenerate Whittaker models on $GL_2(D)$ when $D$ is a quaternion division algebra.
		Merel has proved an important theorem stating that the order of torsion on elliptic curves over a number field are bounded independent of the elliptic curve and the field, and depends only on the degree of the field.
		The paper [28] written with CS Rajan is a re-look at Sunada's theorem about isospectral Riemannian manifolds where we deduce it as a consequence of a simple lemma in group theory.
	www.math.tifr.res.in /~dprasad (2369 words)

	Mathematics
		The principal research interests of the Department lie in the two general areas of mathematical analysis and its applications, and of algebra, mainly representation theory, algebraic geometry, and number theory.
		Automorphic forms: Here the representation theory of these forms was studied from two separate points of view.
		Second, work was finished on analyzing the entirety and boundedness in vertical strips of the automorphic L-functions that appear in constant terms of Eisenstein series a la Langlands.
	www.weizmann.ac.il /acadaff/Scientific_Activities/2000/mathematics.html (1142 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)

	Tonghai Yang (Site not responding. Last check: 2007-11-07)
		Number theory seminar at the University of Minesota, Nov. 30, 1999
		Number theory seminar at Mannheim University, Germany: ``Central Hecke L-values and rank of elliptic cruves.''
		Number theory seminar at the Penn State University: "Nonvanishing of central Hecke L-values and rank zero elliptic curves."
	www.math.sunysb.edu /~thyang/cv.html (512 words)

	Langlands biography
		In a remarkable paper he applied recent results by Harish-Chandra to obtain a formula for the dimension of certain spaces of automorphic forms.
		Then, over the next couple of years, he produced deep results on Eisenstein series and went on to apply Eisenstein series to prove a number theory conjecture due to Weil.
		path-blazing work and extraordinary insights in the fields of number theory, automorphic forms, and group representation.
	www-history.mcs.st-andrews.ac.uk /Biographies/Langlands.html (803 words)

	NEW LISTINGS, NUMBER THEORY WEB
		Number Theory Meeting at the University of Illinois at Urbana-Champaign, May 16-20, 2007, commemorating the 80th birthday of Heini Halberstam (changed date)
		Number Theory Meeting at the University of Illinois at Urbana-Champaign, May 16-20, 2007, commemorating the 80th birthday of Heini Halberstam
		Automorphic forms and zeta functions: Proceedings of a Conference in Memory of Tsuneo Arakawa, Ed.
	www.numbertheory.org /ntw/additions.html (2466 words)

	ARITHMETIC GEOMETRY AND NUMBER THEORY
		Series on Number Theory and Its Applications - Vol.
		Readership: Researchers and graduate students in automorphic representations, number theory, arithmetic algebraic geometry, complex geometry andmathematical physics.
		It is well known that Langlands' theory is fundamentalto automorphic forms, number theory, etc, say via Langlands Program and traceformula that is really the core of the current number theory
	www.worldscibooks.com /mathematics/6115.html (328 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		Professors Langlands and Wiles share the Wolf Prize for their ground-breaking research in modern number theory which has led to the solution of long standing problems as well as defining important new directions.
		Robert P. Langlands has shaped the modern theory of automorphic forms including ground-breaking works on: Eisenstein series, group representations, L-functions and the Artin conjectures, principle of functoriality, and the formulation of the far-reaching Langlands program.
		This problem is responsible for shaping much of number theory in the last two centuries.
	www.wolffund.org.il /full.asp?id=78 (231 words)

	OUP: UK General Catalogue
		His approach to automorphic functions is primarily through the theory of analytic functions.
		The final chapter illustrates the connections between automorphic functions and differential equations with regular singular points, such as the hypergeometric equation.
		The specification in this catalogue, including without limitation price, format, extent, number of illustrations, and month of publication, was as accurate as possible at the time the catalogue was compiled.
	www.oup.com /uk/catalogue/?ci=9780821837412 (282 words)

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