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Arithmetic Dynamics
Arithmetic dynamics is a field that amalgamates two areas of mathematics, dynamical systems and number theory. Part of the inspiration comes from complex dynamics, the study of the Iterated function, iteration of self-maps of the complex plane or other complex algebraic varieties. Arithmetic dynamics is the study of the number-theoretic properties of integer point, integer, rational point, rational, p-adic number, -adic, or algebraic points under repeated application of a polynomial or rational function. A fundamental goal is to describe arithmetic properties in terms of underlying geometric structures. ''Global arithmetic dynamics'' is the study of analogues of classical diophantine geometry in the setting of discrete dynamical systems, while ''local arithmetic dynamics'', also called p-adic dynamics, p-adic or nonarchimedean dynamics, is an analogue of complex dynamics in which one replaces the complex numbers by a -adic field such as or and studies chaotic behavior and the Fa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamical Systems
In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, fluid dynamics, the flow of water in a pipe, the Brownian motion, random motion of particles in the air, and population dynamics, the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured. Time can be measured by integers, by real number, real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be a manifold or simply a Set (mathematics), set, without the need of a Differentiability, smooth space-time structure defined on it. At any given time, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Douglas Northcott
Douglas Geoffrey Northcott, FRS (31 December 1916 – 8 April 2005) was a British mathematician who worked on ideal theory. Early life and career Northcott was born Douglas Geoffrey Robertson in Kensington on 31 December 1916 to Clara Freda (née Behl) (1894–1958) and her first husband Geoffrey Douglas Spence Robertson (1894–1978). His mother remarried in 1919 to Arthur Hugh Kynaston Northcott (1887–1952). In 1935, he legally adopted his step-father's surname. He was educated in London, then at Christ's Hospital and St John's College, Cambridge, where he started research under the supervision of G.H. Hardy. His work was interrupted by active service during World War II. Captured at Singapore, he survived his time as a prisoner of war in Japan, and returned to Cambridge at the end of the war. Back at Cambridge, he published his dissertation "Abstract Tauberian theorems with applications to power series and Hilbert series ". He then turned to algebra under the influence ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Faltings's Theorem
Faltings's theorem is a result in arithmetic geometry, according to which a curve of genus greater than 1 over the field \mathbb of rational numbers has only finitely many rational points. This was conjectured in 1922 by Louis Mordell, and known as the Mordell conjecture until its 1983 proof by Gerd Faltings. The conjecture was later generalized by replacing \mathbb by any number field. Background Let C be a non-singular algebraic curve of genus g over \mathbb. Then the set of rational points on C may be determined as follows: * When g=0, there are either no points or infinitely many. In such cases, C may be handled as a conic section. * When g=1, if there are any points, then C is an elliptic curve and its rational points form a finitely generated abelian group. (This is ''Mordell's Theorem'', later generalized to the Mordell–Weil theorem.) Moreover, Mazur's torsion theorem restricts the structure of the torsion subgroup. * When g>1, according to Faltings's theorem, C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michel Raynaud
Michel Raynaud (; 16 June 1938 – 10 March 2018 Décès de Michel Raynaud Société Mathématique de France.) was a French working in and a professor at Paris-Sud 11 University. Early life and education He was born in Riom, France as a single son to a modest household. His father was a carp ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Manin-Mumford Conjecture
In mathematics, the arithmetic of abelian varieties is the study of the number theory of an abelian variety, or a family of abelian varieties. It goes back to the studies of Pierre de Fermat on what are now recognized as elliptic curves; and has become a very substantial area of arithmetic geometry both in terms of results and conjectures. Most of these can be posed for an abelian variety ''A'' over a number field ''K''; or more generally (for global fields or more general finitely-generated rings or fields). Integer points on abelian varieties There is some tension here between concepts: ''integer point'' belongs in a sense to affine geometry, while ''abelian variety'' is inherently defined in projective geometry. The basic results, such as Siegel's theorem on integral points, come from the theory of diophantine approximation. Rational points on abelian varieties The basic result, the Mordell–Weil theorem in Diophantine geometry, says that ''A''(''K''), the group of points on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shouwu Zhang
Shou-Wu Zhang (; born October 9, 1962) is a Chinese-American mathematician known for his work in number theory and arithmetic geometry. He is currently a Professor of Mathematics at Princeton University. Biography Early life Shou-Wu Zhang was born in Hexian, Ma'anshan, Anhui, China, on October 9, 1962. Zhang grew up in a poor farming household and could not attend school until eighth grade due to the Cultural Revolution. He spent most of his childhood raising ducks in the countryside and self-studying mathematics textbooks that he acquired from sent-down youth in trades for frogs. By the time he entered junior high school at the age of fourteen, he had taught himself calculus and had become interested in number theory after reading about Chen Jingrun's proof of Chen's theorem which made substantial progress on Goldbach's conjecture. Education Zhang was admitted to the Sun Yat-sen University chemistry department in 1980 after scoring poorly on his mathematics entrance examinati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematische Zeitschrift
''Mathematische Zeitschrift'' ( German for ''Mathematical Journal'') is a mathematical journal for pure and applied mathematics published by Springer Verlag. History The journal was founded in 1917, with its first issue appearing in 1918. It was initially edited by Leon Lichtenstein together with Konrad Knopp, Erhard Schmidt, and Issai Schur. Because Lichtenstein was Jewish, he was forced to step down as editor in 1933 under the Nazi rule of Germany; he fled to Poland and died soon after. The editorship was offered to Helmut Hasse Helmut Hasse (; 25 August 1898 – 26 December 1979) was a German mathematician working in algebraic number theory, known for fundamental contributions to class field theory, the application of ''p''-adic numbers to local class field theory and ..., but he refused, Translated by Bärbel Deninger from the 1982 German original. and Konrad Knopp took it over. Other past editors include Erich Kamke, Friedrich Karl Schmidt, Rolf Nevanlinna, Hel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bjorn Poonen
Bjorn Mikhail Poonen (born July 27, 1968, in Boston, Massachusetts) is a mathematician, four-time Putnam Competition winner, and a Distinguished Professor in Science in the Department of Mathematics at the Massachusetts Institute of Technology. His research is primarily in arithmetic geometry, but he has occasionally published in other subjects such as probability and computer science. He has edited two books. He is the founding managing editor of the journal '' Algebra & Number Theory'', and serves also on the editorial boards of '' Involve: A Journal of Mathematics'' and the ''A K Peters Research Notes in Mathematics'' book series.Curriculum vitae retrieved January 28, 2015. Education Poonen is a 1985 alumnus of[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Birch Swinnerton-Dyer Conjecture
In mathematics, the Birch and Swinnerton-Dyer conjecture (often called the Birch–Swinnerton-Dyer conjecture) describes the set of rational solutions to equations defining an elliptic curve. It is an open problem in the field of number theory and is widely recognized as one of the most challenging mathematical problems. It is named after mathematicians Bryan John Birch and Peter Swinnerton-Dyer, who developed the conjecture during the first half of the 1960s with the help of machine computation. Only special cases of the conjecture have been proven. The modern formulation of the conjecture relates to arithmetic data associated with an elliptic curve ''E'' over a number field ''K'' to the behaviour of the Hasse–Weil ''L''-function ''L''(''E'', ''s'') of ''E'' at ''s'' = 1. More specifically, it is conjectured that the rank of the abelian group ''E''(''K'') of points of ''E'' is the order of the zero of ''L''(''E'', ''s'') at ''s'' = 1. The first non-zero c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
LMS Journal Of Computation And Mathematics
''LMS Journal of Computation and Mathematics'' was a peer-reviewed online mathematics journal covering computational aspects of mathematics published by the London Mathematical Society. The journal published its first article in 1998 and ceased operation in 2017. An open access archive of the journal is maintained by Cambridge University Press. Abstracting and indexing The journal is abstracted and indexed in MathSciNet, Scopus, and Zentralblatt MATH zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastru .... References External links * English-language journals Hybrid open access journals Mathematics education in the United Kingdom Computational mathematics journals {{math-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Duke Mathematical Journal
''Duke Mathematical Journal'' is a peer-reviewed mathematics journal published by Duke University Press. It was established in 1935. The founding editors-in-chief were David Widder, Arthur Coble, and Joseph Miller Thomas. The first issue included a paper by Solomon Lefschetz. Leonard Carlitz served on the editorial board for 35 years, from 1938 to 1973. The current managing editor is Richard Hain (Duke University). Impact According to the journal homepage, the journal has a 2018 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a type of journal ranking. Journals with higher impact factor values are considered more prestigious or important within their field. The Impact Factor of a journa ... of 2.194, ranking it in the top ten mathematics journals in the world. References External links * Mathematics journals Mathematical Journal Academic journals established in 1935 Multilingual journals English-language journals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Acta Arithmetica
''Acta Arithmetica'' is a scientific journal of mathematics publishing papers on number theory. It was established in 1935 by Salomon Lubelski and Arnold Walfisz. The journal is published by the Institute of Mathematics of the Polish Academy of Sciences. References External links Online archives (Library of Science, Issues: 1935–2000) 1935 establishments in Poland Number theory journals Academic journals established in 1935 Polish Academy of Sciences academic journals Biweekly journals Academic journals associated with learned and professional societies {{math-journal-stub English-language journals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
