Carl Ludwig Siegel (December 31, 1896 – April 4, 1981) was a German mathematician specialising in number theory. December 31 is the 365th day of the year (366th in leap years) in the Gregorian Calendar. ... 1896 (MDCCCXCVI) was a leap year starting on Wednesday (see link for calendar). ... April 4 is the 94th day of the year in the Gregorian calendar (95th in leap years). ... 1981 (MCMLXXXI) was a common year starting on Thursday of the Gregorian calendar. ... Leonhard Euler is considered by many people to be one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is mathematics. ... To meet Wikipedias quality standards, this article or section may require cleanup. ...

He was born in Berlin, where he enrolled at the Humboldt University in Berlin in 1915 as a student in mathematics, astronomy, and physics. Amongst his teachers were Max Planck and Ferdinand Georg Frobenius, whose influence made the young Siegel abandon astronomy and turn towards number theory instead. For other uses, see Berlin (disambiguation). ... Alternative meaning: Humboldt State University, located in Arcata, California Humboldt-Universität zu Berlin The Humboldt University of Berlin (German Humboldt-Universität zu Berlin) is the successor to Berlins oldest university, the Friedrich Wilhelm University (Friedrich-Wilhelms-Universität), founded in 1810 by the liberal Prussian educational reformer... 1915 (MCMXV) was a common year starting on Friday (see link for calendar). ... Euclid, detail from The School of Athens by Raphael. ... Radio telescopes are among many different tools used by astronomers Astronomy (Greek: αστρονομία = άστρον + νόμος, astronomia = astron + nomos, literally, law of the stars) is the science of celestial objects and phenomena that originate outside the Earths atmosphere, such as stars, planets, comets, auroras, galaxies, and the cosmic background radiation. ... Physics (from the Greek, φυσικός (physikos), natural, and φύσις (physis), nature) is the science of the natural world, which deals with the fundamental constituents of the universe, the forces they exert on one another, and the results of these forces. ... Max Planck Max Karl Ernst Ludwig Planck (April 23, 1858 – October 4, 1947) was one of the most important German physicists of the late 19th and early 20th century; he is considered to be the founder of quantum theory. ... Picture of Frobenius Ferdinand Georg Frobenius (October 26, 1849 - August 3, 1917) was a German mathematician, best-known for his contributions to the theory of differential equations and to group theory. ...

In 1917 he was drafted into the German Army and had to interrupt his studies. After the end of World War I, he enrolled at the University of Göttingen, studying under Edmund Landau, who was his doctoral thesis supervisor (Ph.D. in 1920). He stayed in Göttingen as a teaching and research assistant; many of his groundbreaking results were published during this period. In 1922, he was appointed professor at the University of Frankfurt. 1917 (MCMXVII) was a common year starting on Monday of the Gregorian calendar (see link for calendar) or a common year starting on Tuesday of the 13-day slower Julian calendar. ... The German Army (German: Heer ) is one of three defence units forming the Bundeswehr (Federal Defence Forces) of the Federal Republic of Germany. ... Combatants Allies: Serbia, Russia, France, Romania, Belgium, British Empire, United States, Italy, and others Central Powers: Germany, Austria-Hungary, Bulgaria, Ottoman Empire Casualties Military dead: 5 million Civilian deaths: 3 million Total of dead: 8 million Military dead: 4 million Civilian deaths: 3 million Total dead: 7 million The First... The Georg-August University of Göttingen (Georg-August-Universität Göttingen, often called the Georgia Augusta) was founded in 1734 by George II, King of Great Britain and Elector of Hanover, and opened in 1737. ... Edmund Georg Hermann Landau (February 14, 1877 - February 19, 1938) was a German mathematician and author of over 250 papers on number theory. ... Doctor of Philosophy, or Ph. ... 1920 (MCMXX) was a leap year starting on Thursday (link will take you to calendar) // Events January January 7 - Forces of Russian White admiral Kolchak surrender in Krasnoyarsk. ... 1922 (MCMXXII) was a common year starting on Sunday (see link for calendar). ... University of Frankfurt may refer to two (or three) German universities: the Johann Wolfgang Goethe University Frankfurt am Main (Johann Wolfgang Goethe-Universität Frankfurt am Main) in Frankfurt am Main the European University Viadrina Frankfurt (Oder) (Europa-Universität Viadrina Frankfurt (Oder)) in Frankfurt (Oder), or its historical predecessor which existed...

In 1938, he returned to Göttingen before emigrating in 1940 via Norway to the U.S., where he joined the Institute for Advanced Study at Princeton University, where he had already spent a sabbatical in 1935. He returned to Göttingen only after World War II, when he accepted a post as professor in 1951, which he kept until his retirement in 1959. 1938 (MCMXXXVIII) was a common year starting on Saturday (link will take you to calendar). ... Göttingen ( ) is a city in Lower Saxony, Germany. ... 1940 (MCMXL) was a leap year starting on Monday (the link is to a full 1940 calendar). ... Motto: E pluribus unum (1789 to 1956) (Latin: Out of Many, One) In God We Trust (1956 to present) Anthem: The Star-Spangled Banner Capital Washington, D.C. Largest city New York City Official language(s) None at federal level; English de facto Government • President • Vice President Federal Republic George... Princeton University is a coeducational private university located on an extensive campus in and around suburban Princeton, New Jersey. ... A sabbatical year is a prolonged hiatus, typically one year, in the career of an otherwise successful individual taken in order to fulfill some dream, e. ... 1935 (MCMXXXV) was a common year starting on Tuesday (link will take you to calendar). ... Combatants Allies: Poland, British Commonwealth, France/Free France, Soviet Union, United States, China, and others Axis Powers: Germany, Italy, Japan, and others Casualties Military dead: 17 million Civilian dead: 33 million Total dead: 50 million Military dead: 8 million Civilian dead: 4 million Total dead: 12 million World War II... The meaning of the word professor (Latin: one who claims publicly to be an expert) varies. ... 1951 (MCMLI) was a common year starting on Monday; see its calendar. ... 1959 (MCMLIX) was a common year starting on Thursday of the Gregorian calendar. ...

Siegel's work on number theory and diophantine equations and celestial mechanics in particular won him numerous honours. In 1978, he was awarded the Wolf Prize in Mathematics, one of the most prestigious in the field. To meet Wikipedias quality standards, this article or section may require cleanup. ... In mathematics, a Diophantine equation is a polynomial equation that only allows the variables to be integers. ... Celestial mechanics is a division of astronomy dealing with the motions and gravitational effects of celestial objects. ... 1978 (MCMLXXVIII) was a common year starting on Sunday (the link is to a full 1978 calendar). ... Past winners of the Wolf Prize in Mathematics: 1978 Israel M. Gelfand, Carl L. Siegel 1979 Jean Leray, André Weil 1980 Henri Cartan, Andrei Kolmogorov 1981 Lars Ahlfors, Oscar Zariski 1982 Hassler Whitney, Mark Grigoryevich Krein 1983/4 Shiing S. Chern, Paul Erdős 1984/5 Kunihiko Kodaira, Hans...

Siegel's work spans analytic number theory; and his theorem on the finiteness of the integer points of curves, for genus > 1, is historically important as a major general result on diophantine equations, when the field was essentially undeveloped. He worked on L-functions, discovering the (presumed illusory) Siegel zero phenomenon. His work derived from the Hardy-Littlewood circle method on quadratic forms proved very influential on the later, adele group theories encompassing the use of theta-functions. The Siegel modular forms are recognised as part of the moduli theory of abelian varieties. In all this work the structural implications of analytic methods show through. Analytic number theory is the branch of number theory that uses methods from mathematical analysis. ... A theorem is a proposition that has been or is to be proved on the basis of explicit assumptions. ... In mathematics, Siegels theorem on integral points is the 1929 result of Carl Ludwig Siegel, that for an algebraic curve C of genus g defined over a number field K, presented in affine space in a given coordinate system, there are only finitely many points on C with coordinates... In mathematics, the genus has few different meanings Topology The genus of a connected, oriented surface is an integer representing the maximum number of cuttings along closed simple curves without rendering the resultant manifold disconnected. ... The theory of L-functions has become a very substantial, and still largely conjectural, part of contemporary number theory. ... In mathematics, more specifically in the field of analytic number theory, a Siegel zero, named after Carl Ludwig Siegel, is a type of potential counterexample to the Grand Riemann hypothesis, on the zeroes of Dirichlet L-function. ... In mathematics, the Hardy-Littlewood circle method is one of the most frequently used techniques of analytic number theory. ... In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables. ... In mathematics, an adelic algebraic group is a topological group defined by an algebraic group G over a number field K, and the adele ring A = A(K) of K. It consists of the points of G having values in A; the definition of the appropriate topology is straightforward only... In mathematics, theta functions are special functions of several complex variables. ... In algebraic geometry, the moduli problem is to describe the parameters on which algebraic varieties depend. ... For the purposes of algebraic geometry over the complex numbers, an abelian variety is a complex torus (a torus of real dimension 2n that is a complex manifold) that is also a projective algebraic variety of dimension n, i. ...

See also

• Siegel lemma
• Thue-Siegel-Roth theorem
• Brauer-Siegel theorem
• Siegel upper half-plane
• Siegel-Weil formula

In mathematics, the Thue-Siegel-Roth theorem, also known simply as Roths theorem, is a foundational result in diophantine approximation to algebraic numbers. ... In mathematics, a Siegel upper half-plane is the set of n×n symmetric matrices over the complex number field whose imaginary part is positive definite. ...

External links

• John J. O'Connor and Edmund F. Robertson. Carl Ludwig Siegel at the MacTutor History of Mathematics archive.