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	Atle Selberg - Wikipedia, the free encyclopedia
		Atle Selberg (born June 17, 1917) is a Norwegian mathematician known for his work in analytic number theory, and in the theory of automorphic forms, in particular bringing them into relation with spectral theory.
		Selberg moved to the United States and settled at the Institute for Advanced Study in the 1950s where he remains today.
		This establishes a duality between the length spectrum of a Riemann surface and the eigenvalues of the Laplacian which is analogous to the duality between the prime numbers and the zeros of the zeta function.
	en.wikipedia.org /wiki/Atle_Selberg (302 words)

	Knowledge King - Atle Selberg (Site not responding. Last check: 2007-11-07)
		Atle Selberg, born June 17 1917, a Norwegian mathematician is one of the greatest analytic number theoristss of all time.
		Selberg was born in Langesund, Norway and great work of Srinivasa Aaiyangar Ramanujan influenced on him very soon while he was still at school.
		Selberg and Erdös gave elementary proofs of the prime number theorem, although it was prior believed that such proofs with only real variables can't be found.
	www.knowledgeking.net /encyclopedia/a/at/atle_selberg.html (291 words)

	Selberg trace formula - Wikipedia, the free encyclopedia
		In mathematics, the Selberg trace formula is a central result, or area of research, in non-commutative harmonic analysis.
		The initial publication in 1956 of Atle Selberg dealt with this case, its Laplacian differential operator and its powers.
		In the 1960s the general thrust of the Selberg trace formula, as a piece of analysis, was taken up by the Israel Gelfand school, by Harish-Chandra and Langlands in Princeton, and by Tomio Kubota in Japan.
	en.wikipedia.org /wiki/Selberg_trace_formula (525 words)

	Selberg (Site not responding. Last check: 2007-11-07)
		Selberg used his trace formula to prove that the "Selberg zeta function" of a Riemann surface satisfies an analogue of the Riemann hypothesis.
		Selberg was one of the four editors of Axel Thue's Selected mathematical papers published in Oslo in 1977.
		In 1989 Selberg published Reflections around the Ramanujan centenary which is the text of a talk which he gave at the conclusion of the Ramanujan Centenary Conference in January 1988 at the Tata Institute in Bombay.
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Selberg.html (761 words)

	ATLE SELBERG FACTS AND INFORMATION (Site not responding. Last check: 2007-11-07)
		Atle Selberg (born June_17, 1917) is a Norwegian mathematician known for his work in analytic_number_theory, and in the theory of automorphic_forms, in particular bringing them into relation with spectral_theory.
		Then in 1948 Selberg, working with Paul_ErdÅ‘s, gave an elementary proof of the prime_number_theorem (although there was a dispute between them about to whom this result should primarily be attributed).
		Selberg moved to the United_States and settled at the Institute_for_Advanced_Study in the 1950s where he remains today.
	www.acculegal.com /Atle_Selberg (249 words)

	Atle Selberg (Site not responding. Last check: 2007-11-07)
		Atle Selberg (llevado de junio el 17 de 1917) es matemático noruego, uno de los teóricos analíticos más grandes del número de toda la hora.
		Selberg probó que una mentira positiva de la proporción en esta línea.
		Selberg y Erdös dieron pruebas elementales del teorema primero del número, aunque fue creído anteriormente que tales pruebas con solamente variables verdaderas no pueden ser encontradas.
	www.yotor.net /wiki/es/at/Atle%20Selberg.htm (318 words)

	Riemann hypothesis article - Riemann hypothesis Bernhard Riemann 1859 conjecture zeros Riemann's zeta function - ... (Site not responding. Last check: 2007-11-07)
		However, it was still possible that an infinite number (and possibly the majority) of non-trivial zeros could lie elsewhere in the critical strip.
		Later work by Hardy and Littlewood in 1921 and by Selberg in 1942 gave estimates for the average density of zeros on the critical line.
		Recent work has focused on the explicit calculation of the locations of large numbers of zeros (in the hope of finding a counterexample) and placing upper bounds on the proportion of zeros that can lie away from the critical line (in the hope of reducing this to zero).
	www.what-means.com /encyclopedia/RH (946 words)

	Selberg (Site not responding. Last check: 2007-11-07)
		In 1950 Selberg was awarded a Fields Medal at the International Congress of Mathematicians at Harvard.
		The Fields Medal was awarded for his work on generalisations of the sieve methods of Viggo Brun, and for his major work on the zeros of the Riemann zeta function where he proved that a positive proportion of its zeros satisfy the Riemann hypothesis.
		Selberg is also well known for his elementary proof of the prime number theorem, with a generalisation to prime numbers in an arbitrary arithmetic progression.
	www.bg-rams.ac.at /intranet/Physik/history/Selberg.html (792 words)

	Atle Selberg: Definition and Links by Encyclopedian.com - All about Atle Selberg (Site not responding. Last check: 2007-11-07)
		Atle Selberg: Definition and Links by Encyclopedian.com - All about Atle Selberg
		Atle Selberg, born June 17, 1917, a Norwegian mathematician is one of the greatest analytic number theorists of all time.
		He established the importance of Viggo Brun's sieve methods[?] in number theory, inventing a method that now bears his name, as well as workng on the large sieve[?].
	www.encyclopedian.com /at/Atle-Selberg.html (310 words)

	Citations: the estimation of Fourier coefficients of modular forms - Selberg (ResearchIndex) (Site not responding. Last check: 2007-11-07)
		Selberg, "On the estimation of Fourier coefficients of modular forms", Proc.
		Selberg made the following conjecture to the effect that there are no discrete eigenvalues outside that range other than 0 (coming from the constants) Conjecture 1.2.
		Atle Selberg, On the estimation of Fourier coefficients of modular forms, Proc.
	citeseer.ist.psu.edu /context/137878/0 (1829 words)

	American Mathematical Monthly, The: Ramanujan: Essays and Surveys (Site not responding. Last check: 2007-11-07)
		Selberg begins by recalling how as a boy he read an article on the Indian genius Ramanujan, and how various astonishing identities of Ramanujan inspired him to study similar questions.
		In particular, Selberg was intrigued by the famous Hardy-Ramanujan asymptotic series expansion for p(n), the number of partitions of n.
		Selberg's observation is based on the fact that many of Ramanujan's important discoveries lay in the area of modular forms, a field in which Hecke was an expert, whereas Hardy was not.
	www.findarticles.com /p/articles/mi_qa3742/is_200311/ai_n9318074/pg_2 (1178 words)

	Atle Selberg -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-07)
		Selberg was born in (Click link for more info and facts about Langesund) Langesund, (A constitutional monarchy in northern Europe on the western side of the Scandinavian Peninsula; achieved independence from Sweden in 1905) Norway.
		After the war his accomplishments became known, including a proof that positive proportion of the zeros of the (Click link for more info and facts about Riemann zeta function) Riemann zeta function lie on the line 1/2.
		In a 1947 paper he introduced the Selberg sieve, a method which led to (Click link for more info and facts about Chen's theorem) Chen's theorem among other important results.
	www.absoluteastronomy.com /encyclopedia/a/at/atle_selberg.htm (279 words)

	Encyclopedia: Atle Selberg
		The Fields Medal is a prize awarded to up to four mathematicians (not over forty years of age) at each International Congress of International Mathematical Union, since 1936 and regularly since 1948 at the initiative of the Canadian mathematician John Charles Fields.
		Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers.
		In mathematics, particularly in complex analysis, a Riemann surface is a one-dimensional complex manifold.
	www.nationmaster.com /encyclopedia/Atle-Selberg (1128 words)

	Atle Selberg books ; 0387183892 Misspelled: atle selberg adle selperg selbreg tle ale ate atl atleselberg elberg slberg ...
		Atle Selberg (born June 17, 1917) is a Norwegian mathematician, one of the greatest analyticnumber theorists of all time.Selberg was born in Langesund, Norway.
		This is a famous theorem.He established the importance of Viggo Bruns sieve methods in number theory, inventing a method that now bears his name, as well as working on the large sieve.Selberg came to the United States and settled at the Institute for Advanced Study in the 1950s where he remains today.
		This so-called Selberg trace formula bore a striking resemblance to the explicit formulae, which gave credibility to the speculation of Hilbert and Pólya.Hugh Montgomery investigated and found that the statistical distribution of the zeros on the critical line has a certain property.
	www.americanenglishliterature.com /62300_atle-selberg_0387183892atleselbergcollectedpapersbookcover.html (612 words)

	Atle Selberg (Site not responding. Last check: 2007-11-07)
		Atle Selberg, born June 17, 1917, a Norwegian mathematician is one of the greatest analyticnumber theorists of all time.
		All is still licensed under the GNU FDL.
		His first duty was to go to Constantine Jopp, and speak his regret like a.
	www.termsdefined.net /at/atle-selberg.html (571 words)

	Atle Selberg - Encyclopedia, History, Geography and Biography
		Atle Selberg - Encyclopedia, History, Geography and Biography
		This page was last modified 23:47, 9 May 2005.
		The article about Atle Selberg contains information related to Atle Selberg, See also and External links.
	www.arikah.net /encyclopedia/Atle_Selberg (326 words)

	Atle Selberg - Wikipedia
		Juni 1917 in Langesund, Norwegen) ist ein norwegischer Professor der Mathematik, der 1950 mit der Fields-Medaille für besondere Verdienste um die Mathematik ausgezeichnet wurde.
		Selbergs Interesse an der Mathematik begann bereits als Schüler.
		Atle Selberg Collected Papers: 001 (Springer-Verlag, Heidelberg), ISBN 0387183892
	de.wikipedia.org /wiki/Atle_Selberg (248 words)

	Atle Selberg explained (Site not responding. Last check: 2007-11-07)
		Selberg and Erdős gave elementary proofs of the prime number theorem.
		Before their proof, a proof using only real variables was thought impossible.
		This check Thyrsis paid over story, he sent the balance of the hundred dollars that he owed.
	www.wordspider.net /at/atle-selberg.html (596 words)

	Atle Selberg - Wikipedia
		Atle Selberg, born 1917, is one of the greatest analytic number theorists of all time.
		However Hardy proved that an infinite number of zeros do exist on this line.
		Selberg and Erdos gave elementary proofs of the prime number theorem.
	nostalgia.wikipedia.org /wiki/Atle_Selberg (239 words)

	Selberg, Atle -- Encyclopædia Britannica (Site not responding. Last check: 2007-11-07)
		Selberg attended the University of Oslo (Ph.D., 1943) and remained there as a research fellow until 1947.
		He then became a fellow at the Institute for Advanced Study, Princeton, N.J., U.S., and a member of the faculty from 1949 until his retirement in 1987.
		More results on "Selberg, Atle" when you join.
	www.britannica.com /eb/article-9089363?tocId=9089363 (324 words)

	how Gutzwiller's and Selberg's Trace Formulae are related
		This led to Selberg's trace formula in 1956 which has exactly the same form, but happens to be exact.
		Recall also that the resemblance of the Selberg Trace Formula and the Riemann-Weil explicit formula was the first historical appearance of 'evidence' for the Hilbert-Pólya conjecture, the zeta zeros in the latter corresponding to eigenvalues in the former.
		In this case, however, the relationship between eigenvalues and periodic orbits carries a different name: it is actually known as the Selberg trace formula, because it was first written down by Atle Selberg, a mathematician, over 20 years before physicists became interested in the quantisation of chaotic systems.
	www.maths.ex.ac.uk /~mwatkins/zeta/GTF-STF.htm (1342 words)

	Reminiscences of Paul Erdos
		What Selberg and Erdös did in their "elementary" proofs was to avoid using complex analysis (the proofs were in no sense "easy").
		He told anyone who would listen that Selberg and he had devised an elementary proof of the prime number theorem.
		Selberg later published another elementary proof on his own, and went on to a brilliant mathematical career, eventually becoming a permanent member of the Institute for Advanced Study in Princeton, the Valhalla for mathematicians.
	www.maa.org /features/erdos.html (2908 words)

	Prime number theorem article - Prime number theorem number theory asymptotic prime numbers real number natural ... (Site not responding. Last check: 2007-11-07)
		So-called "elementary proofs" of PNT are available that only use number-theoretic means.
		The first of these was provided partly independently by Paul Erdös and Atle Selberg in 1949.
		It was previously believed by some experts in the field that such proofs could not be found.
	www.what-means.com /encyclopedia/PNT (512 words)

	The Ultimate Hilbert-Pólya conjecture Dog Breeds Information Guide and Reference
		However Selberg in the early 1950s proved a duality between the length spectrum of a Riemann surface and the eigenvalues of its Laplacian.
		This so-called Selberg trace formula bore a striking resemblance to the explicit formulae, which gave credibility to the speculation of Hilbert and Pólya.
		In a development that has given substantive force to this approach to the Riemann hypothesis through functional analysis, Alain Connes has formulated a trace formula that is actually equivalent to a generalized Riemann hypothesis.
	www.dogluvers.com /dog_breeds/Hilbert-Polya_conjecture (355 words)

	Nat' Academies Press, Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics (2003)
		That it might be possible to prove the PNT by elementary methods remained an open issue, but by the time several decades had passed, the general opinion was that no such proof was possible.
		Then, to everybody’s astonishment, such a proof was discovered in 1949 by Atle Selberg, a Norwegian mathematician working at the Institute for Advanced Study in Princeton, New Jersey.
		There was much controversy over the result, because Selberg had communicated some of his preliminary ideas to the eccentric Hungarian mathematician Paul Erdős, who used them to create a proof of his own at the same time.
	www.nap.edu /openbook/0309085497/html/125.html (521 words)

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