|
Schnirelmann's Theorem
In additive number theory, the Schnirelmann density of a sequence of numbers is a way to measure how "dense" the sequence is. It is named after Russian mathematician Lev Schnirelmann, who was the first to study it.Schnirelmann, L.G. (1930).On the additive properties of numbers, first published in "Proceedings of the Don Polytechnic Institute in Novocherkassk" (in Russian), vol XIV (1930), pp. 3-27, and reprinted in "Uspekhi Matematicheskikh Nauk" (in Russian), 1939, no. 6, 9–25.Schnirelmann, L.G. (1933). First published asÜber additive Eigenschaften von Zahlen in "Mathematische Annalen" (in German), vol 107 (1933), 649-690, and reprinted asOn the additive properties of numbers in "Uspekhin. Matematicheskikh Nauk" (in Russian), 1940, no. 7, 7–46. Definition The Schnirelmann density of a set of natural numbers ''A'' is defined as :\sigma A = \inf_n \frac, where ''A''(''n'') denotes the number of elements of ''A'' not exceeding ''n'' and inf is infimum.Nathanson (1996) pp.191–1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Additive Number Theory
Additive number theory is the subfield of number theory concerning the study of subsets of integers and their behavior under addition. More abstractly, the field of additive number theory includes the study of abelian groups and commutative semigroups with an operation of addition. Additive number theory has close ties to combinatorial number theory and the geometry of numbers. Two principal objects of study are the sumset of two subsets ''A'' and ''B'' of elements from an abelian group ''G'', :A + B = \, and the h-fold sumset of ''A'', :hA = \underset\,. Additive number theory The field is principally devoted to consideration of ''direct problems'' over (typically) the integers, that is, determining the structure of ''hA'' from the structure of ''A'': for example, determining which elements can be represented as a sum from ''hA'', where ''A'' is a fixed subset.Nathanson (1996) II:1 Two classical problems of this type are the Goldbach conjecture (which is the conjecture that 2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Henry Mann
Henry Berthold Mann (27 October 1905, Vienna – 1 February 2000, Tucson) was a professor of mathematics and statistics at the Ohio State University. Mann proved the Schnirelmann-Landau conjecture in number theory, and as a result earned the 1946 Cole Prize. He and his student developed the ("Mann-Whitney") ''U''-statistic of nonparametric statistics. (The web-link is to a slightly updated edition of the biography.) Mann published the first mathematical book on the design of experiments: . Early life of a number theorist Born in Vienna, Austria-Hungary, to a Jewish family, Mann earned his Ph.D. degree in mathematics in 1935 from the University of Vienna under the supervision of Philipp Furtwängler. Mann immigrated to the United States in 1938, and lived in New York, supporting himself by tutoring students. In additive number theory, Mann proved the Schnirelmann–Landau conjecture on the asymptotic density of sumsets in 1942. By doing so he established Mann's theorem and earne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematische Annalen
''Mathematische Annalen'' (abbreviated as ''Math. Ann.'' or, formerly, ''Math. Annal.'') is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann. Subsequent managing editors were Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguignon, Wolfgang Lück, and Nigel Hitchin. Currently, the managing editor of Mathematische Annalen is Thomas Schick. Volumes 1–80 (1869–1919) were published by Teubner. Since 1920 (vol. 81), the journal has been published by Springer. In the late 1920s, under the editorship of Hilbert, the journal became embroiled in controversy over the participation of L. E. J. Brouwer on its editorial board, a spillover from the foundational Brouwer–Hilbert controversy. Between 1945 and 1947 the journal briefly ceased publication. References External links''Mathematische Annalen''homepage at Springer''Mathematische Annalen''archive (1869†... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Imre Z
Imre is a Hungarian masculine first name, which is also in Estonian use, where the corresponding name day is 10 April. It has been suggested that it relates to the name Emeric, Emmerich or Heinrich. Its English equivalents are Emery and Henry. Bearers of the name include the following (who generally held Hungarian nationality, unless otherwise noted): *Imre Antal (1935–2008), pianist *Imre Bajor (1957–2014), actor * Imre Bebek (d. 1395), baron *Imre Bródy (1891–1944), physicist * Imre Bujdosó (b. 1959), Olympic fencer *Imre Csáky (cardinal) (1672–1732), Roman Catholic cardinal * Imre Csermelyi (b. 1988), football player *Imre Cseszneky (1804–1874), agriculturist and patriot *Imre Csiszár (b. 1938), mathematician * Imre Csösz (b. 1969), Olympic judoka *Imre Czobor (1520–1581), Noble and statesman *Imre Czomba (b. 1972), Composer and musician *Imre Deme (b. 1983), football player *Imre Erdődy (1889–1973), Olympic gymnast * Imre Farkas (1879–1976), musician ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eduard Wirsing
Eduard Wirsing (28 June 1931 – 22 March 2022) was a German mathematician, specializing in number theory. Biography Wirsing was born on 28 June 1931 in Berlin. Wirsing studied at the University of Göttingen and the Free University of Berlin, where he received his doctorate in 1957 under the supervision of Hans-Heinrich Ostmann with thesis ''Über wesentliche Komponenten in der additiven Zahlentheorie'' (On Essential Components in Additive Number Theory). In 1967/68 he was a professor at Cornell University and from 1969 a full professor at the University of Marburg, where he was since 1965. In 1970/71 he was at the Institute for Advanced Study. Since 1974 he was a professor at the University of Ulm, where he led the 1976 Mathematical Colloquium. He retired as professor emeritus in 1999, but continued to be mathematically active. Wirsing organized conferences on analytical number theory at the Oberwolfach Research Institute for Mathematics. In his spare time he played go and ch ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
