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Kurt Heegner
Kurt Heegner (; 16 December 1893 – 2 February 1965) was a German private scholar from Berlin, who specialized in radio engineering and mathematics. He is famous for his mathematical discoveries in number theory and, in particular, the Stark–Heegner theorem. Life and career Heegner was born and died in Berlin. In 1952, he published the Stark–Heegner theorem which he claimed was the solution to a classic number theory problem proposed by the great mathematician Gauss, the class number 1 problem. Heegner's work was not accepted for years, mainly due to his quoting of a portion of Heinrich Martin Weber's work that was known to be incorrect (though he never used this result in the proof). Heegner's proof was accepted as essentially correct after a 1967 announcement by Bryan Birch, and definitively resolved by a paper by Harold Stark that had been delayed in publication until 1969 (Stark had independently arrived at a similar proof, but disagrees with the common notion that h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radio
Radio is the technology of signaling and communicating using radio waves. Radio waves are electromagnetic waves of frequency between 30 hertz (Hz) and 300 gigahertz (GHz). They are generated by an electronic device called a transmitter connected to an antenna which radiates the waves, and received by another antenna connected to a radio receiver. Radio is very widely used in modern technology, in radio communication, radar, radio navigation, remote control, remote sensing, and other applications. In radio communication, used in radio and television broadcasting, cell phones, two-way radios, wireless networking, and satellite communication, among numerous other uses, radio waves are used to carry information across space from a transmitter to a receiver, by modulating the radio signal (impressing an information signal on the radio wave by varying some aspect of the wave) in the transmitter. In radar, used to locate and track objects like aircraft, ships, sp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harold Stark
Harold Mead Stark (born August 6, 1939 in Los Angeles, California) is an American mathematician, specializing in number theory. He is best known for his solution of the Gauss class number 1 problem, in effect correcting and completing the earlier work of Kurt Heegner, and for Stark's conjecture. More recently, he collaborated with Audrey Terras to study zeta functions in graph theory. He is currently on the faculty of the University of California, San Diego. Stark received his bachelor's degree from California Institute of Technology in 1961 and his PhD from the University of California, Berkeley in 1964. He was on the faculty at the University of Michigan from 1964 to 1968, at the Massachusetts Institute of Technology from 1968 to 1980, and at the University of California, San Diego from 1980 to the present. Stark was elected to the American Academy of Arts and Sciences in 1983 and to the United States National Academy of Sciences in 2007. In 2012, he became a fellow of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1893 Births
Events January–March * January 2 – Webb C. Ball introduces railroad chronometers, which become the general railroad timepiece standards in North America. * Mark Twain started writing Puddn'head Wilson. * January 6 – The Washington National Cathedral is chartered by Congress; the charter is signed by President Benjamin Harrison. * January 13 ** The Independent Labour Party of the United Kingdom has its first meeting. ** U.S. Marines from the ''USS Boston'' land in Honolulu, Hawaii, to prevent the queen from abrogating the Bayonet Constitution. * January 15 – The ''Telefon Hírmondó'' service starts with around 60 subscribers, in Budapest. * January 17 – Overthrow of the Kingdom of Hawaii: Lorrin A. Thurston and the Citizen's Committee of Public Safety in Hawaii, with the intervention of the United States Marine Corps, overthrow the government of Queen Liliuokalani. * January 21 ** The Cherry Sisters first perform in Marion, Iowa. ** The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Number Theory
The ''Journal of Number Theory'' (''JNT'') is a bimonthly peer-reviewed scientific journal covering all aspects of number theory. The journal was established in 1969 by R.P. Bambah, P. Roquette, A. Ross, A. Woods, and H. Zassenhaus (Ohio State University). It is currently published monthly by Elsevier and the editor-in-chief is Dorian Goldfeld (Columbia University). According to the ''Journal Citation Reports'', the journal has a 2020 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as ... of 0.72. References External links * Number theory Mathematics journals Publications established in 1969 Elsevier academic journals Monthly journals English-language journals {{math-journal-stub ... [...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. It was founded in 1918 and edited by Leon Lichtenstein together with Konrad Knopp, Erhard Schmidt, and Issai Schur. Past editors include Erich Kamke, Friedrich Karl Schmidt, Rolf Nevanlinna, Helmut Wielandt __NOTOC__ Helmut Wielandt (19 December 1910 – 14 February 2001) was a German mathematician who worked on permutation groups. He was born in Niedereggenen, Lörrach, Germany. He gave a plenary lecture ''Entwicklungslinien in der Strukturtheorie d ..., and Olivier Debarre. External links * * Mathematics journals Publications established in 1918 {{math-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heegner's Lemma
In mathematics, Heegner's lemma is a lemma used by Kurt Heegner Kurt Heegner (; 16 December 1893 – 2 February 1965) was a German private scholar from Berlin, who specialized in radio engineering and mathematics. He is famous for his mathematical discoveries in number theory and, in particular, the Stark–He ... in his paper on the class number problem. His lemma states that if :y^2=a_4x^4+a_3x^3+a_2x^2+a_1x+a_0 is a curve over a field with ''a''4 not a square, then it has a solution if it has a solution in an extension of odd degree. References * Diophantine equations Lemmas in number theory {{numtheory-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heegner Point
In mathematics, a Heegner point is a point on a modular curve that is the image of a quadratic imaginary point of the upper half-plane. They were defined by Bryan Birch and named after Kurt Heegner, who used similar ideas to prove Gauss's conjecture on imaginary quadratic fields of class number one. Gross–Zagier theorem The Gross–Zagier theorem describes the height of Heegner points in terms of a derivative of the L-function of the elliptic curve at the point ''s'' = 1. In particular if the elliptic curve has (analytic) rank 1, then the Heegner points can be used to construct a rational point on the curve of infinite order (so the Mordell–Weil group has rank at least 1). More generally, showed that Heegner points could be used to construct rational points on the curve for each positive integer ''n'', and the heights of these points were the coefficients of a modular form of weight 3/2. Shou-Wu Zhang generalized the Gross–Zagier theorem from elliptic cur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heegner Number
In number theory, a Heegner number (as termed by Conway and Guy) is a square-free positive integer ''d'' such that the imaginary quadratic field \Q\left sqrt\right/math> has class number 1. Equivalently, its ring of integers has unique factorization. The determination of such numbers is a special case of the class number problem, and they underlie several striking results in number theory. According to the (Baker–)Stark–Heegner theorem there are precisely nine Heegner numbers: This result was conjectured by Gauss and proved up to minor flaws by Kurt Heegner in 1952. Alan Baker and Harold Stark independently proved the result in 1966, and Stark further indicated the gap in Heegner's proof was minor. Euler's prime-generating polynomial Euler's prime-generating polynomial n^2 + n + 41, which gives (distinct) primes for ''n'' = 0, ..., 39, is related to the Heegner number 163 = 4 · 41 − 1. Rabinowitz proved that n^ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Amateur Mathematicians
This is a list of amateur mathematicians—people whose primary vocation did not involve mathematics (or any similar discipline) yet made notable, and sometimes important, contributions to the field of mathematics. *Ahmes (scribe) *Ashutosh Mukherjee (lawyer) *Robert Ammann (programmer and postal worker) * John Arbuthnot (surgeon and author) * Jean-Robert Argand (shopkeeper) *Leon Bankoff (Beverly Hills dentist) * Rev. Thomas Bayes (Presbyterian minister) *Andrew Beal (businessman) *Isaac Beeckman (candlemaker) *Chester Ittner Bliss (biologist) *Napoléon Bonaparte (general) *Mary Everest Boole (homemaker, librarian) * William Bourne (innkeeper) *Nathaniel Bowditch (indentured bookkeeper) * Achille Brocot (clockmaker) *Jost Bürgi (clockmaker) * Marvin Ray Burns (veteran) *Gerolamo Cardano (medical doctor) *D. G. Champernowne (college student) * Thomas Clausen (technical assistant) * Sir James Cockle (judge) *Federico Commandino (medical doctor) * Herb Conn (rock climber) *Willia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bryan Birch
Bryan John Birch FRS (born 25 September 1931) is a British mathematician. His name has been given to the Birch and Swinnerton-Dyer conjecture. Biography Bryan John Birch was born in Burton-on-Trent, the son of Arthur Jack and Mary Edith Birch. He was educated at Shrewsbury School and Trinity College, Cambridge. He married Gina Margaret Christ in 1961. They have three children. As a doctoral student at the University of Cambridge, he was officially working under J. W. S. Cassels. More influenced by Harold Davenport, he proved Birch's theorem, one of the results to come out of the Hardy–Littlewood circle method. He then worked with Peter Swinnerton-Dyer on computations relating to the Hasse–Weil L-functions of elliptic curves. Their subsequently formulated conjecture relating the rank of an elliptic curve to the order of zero of an L-function has been an influence on the development of number theory from the mid-1960s onwards. only partial results have been obtained. He ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Engineering
Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more specialized fields of engineering, each with a more specific emphasis on particular areas of applied mathematics, applied science, and types of application. See glossary of engineering. The term ''engineering'' is derived from the Latin ''ingenium'', meaning "cleverness" and ''ingeniare'', meaning "to contrive, devise". Definition The American Engineers' Council for Professional Development (ECPD, the predecessor of ABET) has defined "engineering" as: The creative application of scientific principles to design or develop structures, machines, apparatus, or manufacturing processes, or works utilizing them singly or in combination; or to construct or operate the same with full cognizance of their design; or to forecast their behavior under speci ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heinrich Martin Weber
Heinrich Martin Weber (5 March 1842, Heidelberg, Germany – 17 May 1913, Straßburg, Alsace-Lorraine, German Empire, now Strasbourg, France) was a German mathematician. Weber's main work was in algebra, number theory, and analysis. He is best known for his text ''Lehrbuch der Algebra'' published in 1895 and much of it is his original research in algebra and number theory. His work ''Theorie der algebraischen Functionen einer Veränderlichen'' (with Dedekind) established an algebraic foundation for Riemann surfaces, allowing a purely algebraic formulation of the Riemann–Roch theorem. Weber's research papers were numerous, most of them appearing in ''Crelle's Journal'' or ''Mathematische Annalen''. He was the editor of Riemann's collected works. Weber was born in Heidelberg, Baden, and entered the University of Heidelberg in 1860. In 1866 he became a privatdozent, and in 1869 he was appointed as extraordinary professor at that school. Weber also taught in Zurich at the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
