
	Where results make sense

Topic: Erich Hecke

	Hecke operator - Wikipedia, the free encyclopedia
		In mathematics, in particular in the theory of modular forms, a Hecke operator is a certain kind of 'averaging' operator that plays a significant role in the structure of vector spaces of modular forms (and more general automorphic representations).
		The theory of Hecke operators on modular forms is often said to have been founded by Mordell in a paper on the special cusp form of Ramanujan, ahead of the general theory given by Erich Hecke.
		In the classical elliptic modular form theory it is shown that the Hecke operators are a C-star algebra with respect to the Peterson inner product; and that therefore the spectral theory implies that there is a basis of modular forms that are eigenfunctions for all Hecke operators.
	en.wikipedia.org /wiki/Hecke_operator (454 words)

	Erich Hecke - Wikipedia, the free encyclopedia
		Erich Hecke (September 20, 1887 – February 13, 1947) was a German mathematician.
		He devoted most of his research to the theory of modular forms, creating the general theory of cusp forms (holomorphic, for GL(2)), as it is now understood in the classical setting.
		The method extended to the L-functions associated to a class of characters now known as Hecke characters or idele class characters: such L-functions are now known as Hecke L-functions.
	en.wikipedia.org /wiki/Erich_Hecke (142 words)

	Hecke (Site not responding. Last check: 2007-10-26)
		Hecke was awarded his doctorate at Göttingen in 1910 for a dissertation Zur Theorie der Modulfunktionen von zwei Variablen und ihrer Anwendung auf die Zahlentheorie which had been supervised by Hilbert.
		Hecke remained at Göttingen where he was appointed as an assistant to Hilbert and Klein.
		Probably Hecke's most important work was in 1936 with his discovery of the properties of the algebra of Hecke operators and of the Euler products associated with them.
	www-history.mcs.st-and.ac.uk /~history/Mathematicians/Hecke.html (759 words)

	Mathematik in Göttingen: Erich Hecke
		Hecke wurde von diesen Überlegungen zu einigen Fragen der analytischen Zahlentheorie geführt.
		Hecke wurde durch diese Untersuchungen zu der Theorie der Modulformen geleitet.Er konstruierte zum ersten Mal Modulformen, die indefiniten quadratischen Formen zugeordnet sind.
		Hecke scheint von deren Arbeit nichts gewußt zu haben, und seine Ergebnisse sind viel allgemeiner.
	www.math.uni-goettingen.de /Personen/Bedeutende_Mathematiker/hecke.html (588 words)

	erich in directory.co.uk
		Erich Maria Remarque was born in Osnabruck, Germany, in 1898.
		Erich Fromm was born in 1900 in Frankfurt, Germany.
		Erich Hauser was born in 1930 in Rietheim, Germany.
	msxml.infospace.com /_1_28DOTFE06KNWFE__uk.drctuk/search/web/erich/1/20/1/-/1/0/1/1/1/1?engineset=uk-only (332 words)

	Hecke (Site not responding. Last check: 2007-10-26)
		Erich Hecke's father, Heinrich Hecke, was an architect.
		Erich attended primary school at Buk before going to Posen for his secondary school studies.
		Hecke, however, was happy with his new post at Hamburg and turned down the offer from Berlin.
	www-history.mcs.st-andrews.ac.uk /Mathematicians/Hecke.html (759 words)

	Mielke, Erich -- Encyclopædia Britannica (Site not responding. Last check: 2007-10-26)
		On January 12 a Berlin court dropped manslaughter charges against Erich Honecker, the former communist leader of East Germany, in connection with the shoot-to-kill policy that had claimed hundreds of lives at the Berlin Wall and on the inner-German border.
		Erich Leinsdorf had some of his first successes in opera but later worked mainly with orchestras.
		Erich Mendelsohn was known for his pioneering work in steel and concrete.
	www.britannica.com /eb/article-9344015 (619 words)

	Ludendorff, Erich von -- Britannica Student Encyclopedia
		Erich von Ludendorff was born on April 9, 1865, in Prussia.
		An expert strategist, Ludendorff worked with Paul von Hindenburg in World War I and with him was responsible for many successful campaigns in the late years of the war.
		An acclaimed motion picture director of the 1920s and 1930s, Erich von Stroheim is best known for the unbending realism and perfection of detail in his films.
	www.britannica.com /ebi/article-9312247 (636 words)

	The Proof of Fermat's Last Theorem
		There are certain operators called Hecke operators, after Erich Hecke, on spaces of modular forms, and for the subspace S(N) in particular, since they preserve the weight of a form.
		Hecke operators can be defined concretely in various ways.
		S(N) is a normalized eigenform of all Hecke operators, it can in fact be shown that the coefficients in the Fourier expansion are all algebraic numbers and that they generate a finite extension K of Q.
	www.mbay.net /~cgd/flt/flt08.htm (1543 words)

	Modular form -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-26)
		Modular form theory is a special case of the more general theory of (additional info and facts about automorphic form) automorphic forms, and therefore can now be seen as just the most concrete part of a rich theory of (additional info and facts about discrete group) discrete groups.
		The term modular form, as a systematic description, is usually attributed to Hecke.
		theory of (additional info and facts about Hecke operator) Hecke operators, which also gives the link between the theory of modular forms and (additional info and facts about representation theory) representation theory.
	www.absoluteastronomy.com /encyclopedia/m/mo/modular_form.htm (2048 words)

	Geometry.Net - Scientists: Hecke Erich
		Born 20 Sept 1887 in Buk Erich Hecke's father, HeinrichHecke, was an architect.
		The paper [5] is a published version of a talk given by Schoeneberg at a conference organised in Hamburg to celebrate the 100th anniversary of Hecke's birthday in 1987.
		Hecke Erich Ãber Dirichlet- Reihen mit Funktionsgleichung und ihre Nullstellen auf der Mittelgraden
	www.geometry.net /detail/scientists/hecke_erich.html (801 words)

	Citebase - Hecke operators on rational functions
		It turns out that the simultaneous eigenfunctions of all of the Hecke operators involve Dirichlet characters mod L, giving rise to the result that any arithmetic function of m that is completely multiplicative and also satisfies a linear recurrence must be a Dirichlet character times a power of m.
		Ricardo Diaz and Sinai Robins, The Ehrhart polynomial of a lattice polytope, Ann.
		Erich Hecke, Analytische Arithmetik der positiven quadratischen Formen, Danske Vid.
	www.citebase.org /cgi-bin/citations?id=oai:arXiv.org:math/0309244 (423 words)

	[No title]
		Erich Hecke: Ueber die Bestimmung Dirichletscher Reihen durch ihre Funktionalgleichung.
		Erich Hecke: Ueber die Modulfunktionen und die Dirichletschen Reihen mit Eulerscher Produktentwicklung I-II.
		Gives among other things a very clear (but brief) introduction to the theory of Hecke operators and to the applications of theta series to the arithmetic of quadratic forms.
	felix.unife.it /Root/d-Mathematics/d-Number-theory/b-Modular-and-automorphic-functions (1549 words)

	Erich Fromm -- Encyclopædia Britannica
		More results on "Erich Fromm" when you join.
		The psychoanalyst and social philosopher Erich Fromm, for example, argued that freedom was stressful (see Fromm).
		Short biography of Hanna Fromm, focusing on her founding of the Fromm Institute For Lifelong Learning at the University of San Francisco.
	www.britannica.com /eb/article-9035492 (607 words)

	Louis Mordell - Slider
		During World War I he was involved in war work, but also produced one of his major results, proving in 1917 the multiplicative property of Ramanujan's tau-function.
		The proof was by means, in effect, of the Hecke operators, which had not yet been christened for Erich Hecke; it was, in retrospect, one of the major advances in modular form theory, beyond its status as an odd corner of the theory of special functions.
		In 1920 he took a teaching position in Manchester College of Technology, becoming Reader at the Victoria University of Manchester in 1922 and Professor in 1923.
	enc.slider.com /Enc/L._J._Mordell (380 words)

	Abstract for 2002/10/21: Russo (Site not responding. Last check: 2007-10-26)
		A Hecke correspondence is an association between entire modular (or automorphic) forms and Dirichlet series satisfying a prescribed functional equation.
		In the mid 1930's, Erich Hecke clarified the connection by way of the Mellin transform.
		In this talk, we will use a variation of the Mellin transform to discuss a Hecke correspondence theorem on certain classes of conjugates (by real 2×2 matrices of determinant one) of the Hecke groups.
	www.math.binghamton.edu /MATH/dept/ComboSem/abstract.200210rus.html (194 words)

	Langlands program biography .ms (Site not responding. Last check: 2007-10-26)
		The insight of Langlands was to find the proper generalization of Dirichlet L-functions which would allow the formulation of Artin's statement in this more general setting.
		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).
		Langlands then generalized these to automorphic cuspidal representations, which are certain infinite dimensional irreducible representations of the general linear group GL n
	www.biography.ms /Langlands_program.html (810 words)

	Functional equation (L function) (Site not responding. Last check: 2007-10-26)
		A unified theory of such functional equations was given by Erich Hecke, and the theory taken up again in Tate's thesis by John Tate.
		now called Hecke characters, for which hisproof (based on theta functions) also worked.
		These characters andtheir associated L-functions are now understood to be strictly related to complex multiplication, as the Dirichlet characters are to cyclotomic fields.
	www.therfcc.org /functional-equation-l-function--218248.html (552 words)

	[No title]
		Erich Hecke established the basic properties of Dirichlet L-functions in 1936, including a special symmetry called the "functional equation" which Riemann had already shown for his zeta function.
		So I bet Hecke must have dreamt of the Generalized Riemann Hypothesis, even if he didn't dare state it.
		Hecke also proved a functional equation for these back in 1936.
	math.ucr.edu /home/baez/twf_ascii/week217 (4253 words)

	Problems in Ballistics
		After serving in the German navy during World War I, Hasse matriculated at the University of Göttingen in 1918.
		There he attended lectures of Edmund Landau, David Hilbert, Emmy Noether, and Erich Hecke.
		In 1820, Hasse went to Marburg, and under the direction of Kurt Hensel, discovered what is now known as the Hasse principle, or "local-global" principle, in algebraic number theory.
	www.explosionmodel.net /p2_2.html (254 words)

	References for Hecke (Site not responding. Last check: 2007-10-26)
		S J Patterson, Erich Hecke und die Rolle der L-Reihen in der Zahlentheorie, Ein Jahrhundert Mathematik 1890-1990, Dokumente Gesch.
		H Petersson, Das wissenschaftliche Werk von E Hecke, Abhandlungen aus dem Mathematischen Seminar, Universität Hamburg 16 (1949), 7-31.
		B Schoeneberg, Erich Hecke 1887-1947, Jahresberichte der Deutschen Mathematiker-Vereinigung 91 (1989), 168-190.
	www-gap.dcs.st-and.ac.uk /~history/References/Hecke.html (58 words)

	Omega
		Hecke discovered an amazing connection between each modular form and a corresponding Dirichlet L-series.
		In 1937 Erich Hecke showed (also see the above) that if the Fourier coefficients of a modular cusp form are plugged into a Dirichlet L-series, then that series can be uniquely factored into an Euler product, i.e.
		It was mainly Taniyama who connected the elliptic and modular functions, and his result was used by Wiles to prove Fermat.
	mywebpages.comcast.net /dantsmith/nexu38.htm (11764 words)

	MIT Libraries' catalog - Barton - Full Catalog - Full Record
		Academic Mathematical Life -- Erich Bessel-Hagen and the General Atmosphere -- Dozentenschaft Reports -- Foreign Contact and Travel -- Mathematical Camps -- Students and Faculty Before and During Wartime -- The Value of Mathematics in the Nazi State -- Secondary and Elementary Mathematics -- The Wartime Drafting of Scientists -- Ch.
		Germans and Jews -- Wilhelm Blaschke -- The Development of Heinrich Behnke’s Attitudes -- Erich Hecke -- Oswald Teichmuller -- Ernst Witt -- Richard Courant -- Edmund Landau -- Felix Hausdorff -- Ernst Peschl -- Paul Riebesell --
		Erich Kahler -- Wilhelm Suss -- The Positions of German Mathematicians.
	library.mit.edu /F?func=find-b&find_code=SYS&request=001286289 (274 words)

	Die schönsten Tiergeschichten - Hans Hecke Testbericht - Für Tierfreunde (Site not responding. Last check: 2007-10-26)
		Die schönsten Tiergeschichten - Hans Hecke » Testbericht
		Bei diesen Buch handelt es sich um eine Sonderausgabe und ist für die Jugend von Hans Hecke zusammengestellt worden und herausgebracht wurde diese Buch vom TOSA —Verlag, Wien dieser Verlag besteht immer noch.
		Titel des Buches Die schönsten Tiergeschichten und hat eine Seiten Zahl von 413.
	www.yopi.de /erfahrungsbericht_149751__Fuer_Tierfreunde (837 words)

	erich in directory.co.uk
		Web results for "erich" (1 - 20 of 51)
		Erich (1887-1973) IDENTITY STATEMENT Reference code(s): GB 0099 KCLMA Von Manstein...
		Erich von Daniken, author of Chariot of the Gods and more than two dozen 'true-life' accounts of alien visitation, is set to join the...
	msxml.infospace.com /_1_2LV1TFE04TV4JF6__uk.drctuk/search/web/erich/1/20/1/-/1/0/1/1/1/1?engineset=uk-only (362 words)

	Biographien, Virtueller Stadtrundgang in Hamburg - Kulturgeschichte, Naturwissenschaft und Technik - Institut für ...
		Chern, Shiing Shen (* 28.10.1911) - chinesischer Mathematiker, in den 1930er Jahren in Hamburg (Wilhelm Blaschke, Erich Kähler, Emil Artin, Erich Hecke)
		Hecke, Erich (1887-1947) - Mathematiker, Professor an der Universität Hamburg 1919-1947
		Kaluznin, Lev Arkad'evich (1914-1990) - Mathematiker, studierte 1936-1938 in Hamburg bei Artin, Hecke und Zassenhaus
	www.math.uni-hamburg.de /math/ign/hh/1bio.htm (3075 words)

	Erich Hecke (Site not responding. Last check: 2007-10-26)
		Hecke, Erich Hecke, Erich Hecke, Erich Hecke, Erich
		You can click on this message to see their list of those items.
		Sorry, no screened links relevant to Erich Hecke were found:
	www.omniknow.com /common/wiki.php?in=en&term=Erich_Hecke (307 words)

	Bulletin of the American Mathematical Society
		Erich Hecke, Lectures on Dirichlet series, modular functions and quadratic forms, Vandenhoeck and Ruprecht, Göttingen, 1983, Edited by Bruno Schoeneberg; With the collaboration of Wilhelm Maak.
		Richard Taylor and Andrew Wiles, Ring-theoretic properties of certain Hecke algebras, Ann.
		E. Titchmarsh, The theory of the Riemann zeta-function, 2nd ed., The Clarendon Press Oxford University Press, New York, 1986, Edited and with a preface by D. Heath-Brown.
	www.ams.org /bull/2004-41-01/S0273-0979-03-00995-9/home.html (2686 words)

Try your search on: Qwika (all wikis)