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Harold Stark
Harold Mead Stark (born August 6, 1939) is an Americans, American mathematician, specializing in number theory. He is best known for his solution of the Carl Friedrich Gauss, Gauss class number 1 problem, in effect Stark–Heegner theorem, correcting and completing the earlier work of Kurt Heegner, and for Stark's conjecture. More recently, he collaborated with Audrey Terras to study Ihara zeta function, 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 the 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians was Thales of Miletus (); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales's theorem. The number of known mathematicians grew when Pythagoras of Samos () established the Pythagorean school, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1939 Births
This year also marks the start of the World War II, Second World War, the largest and deadliest conflict in human history. Events Events related to World War II have a "WWII" prefix. January * January 1 ** Coming into effect in Nazi Germany of: *** The Protection of Young Persons Act (Germany), Protection of Young Persons Act, passed on April 30, 1938, the Working Hours Regulations. *** The small businesses obligation to maintain adequate accounting. *** The Jews name change decree. ** With his traditional call to the New Year in Nazi Germany, Führer and Reich Chancellor Adolf Hitler addresses the members of the National Socialist German Workers' Party (NSDAP). ** The Hewlett-Packard technology and scientific instruments manufacturing company is founded by Bill Hewlett and David Packard, in a garage in Palo Alto, California, considered the birthplace of Silicon Valley. ** Philipp Etter takes over as President of the Swiss Confederation. ** The Third Soviet Five Year P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brumer–Stark Conjecture
The Brumer–Stark conjecture is a conjecture in algebraic number theory giving a rough generalization of both the analytic class number formula for Dedekind zeta functions, and also of Stickelberger's theorem about the factorization of Gauss sums. It is named after Armand Brumer and Harold Stark. It arises as a special case (abelian and first-order) of Stark's conjecture, when the place that splits completely in the extension is finite. There are very few cases where the conjecture is known to be valid. Its importance arises, for instance, from its connection with Hilbert's twelfth problem. Statement of the conjecture Let be an abelian extension of global fields, and let be a set of places of containing the Archimedean places and the prime ideals that ramify in . The -imprimitive equivariant Artin L-function is obtained from the usual equivariant Artin L-function by removing the Euler factors corresponding to the primes in from the Artin L-functions from which th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs. The society is one of the four parts of the Joint Policy Board for Mathematics and a member of the Conference Board of the Mathematical Sciences. History The AMS was founded in 1888 as the New York Mathematical Society, the brainchild of Thomas Fiske, who was impressed by the London Mathematical Society on a visit to England. John Howard Van Amringe became the first president while Fiske became secretary. The society soon decided to publish a journal, but ran into some resistance over concerns about competing with the '' American Journal of Mathematics''. The result was the ''Bulletin of the American Mathematical Society'', with Fiske as editor-in-chief. The de facto journal, as intended, was influentia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
California Institute Of Technology
The California Institute of Technology (branded as Caltech) is a private research university in Pasadena, California, United States. The university is responsible for many modern scientific advancements and is among a small group of institutes of technology in the United States that are devoted to the instruction of pure and applied sciences. The institution was founded as a preparatory and vocational school by Amos G. Throop in 1891 and began attracting influential scientists such as George Ellery Hale, Arthur Amos Noyes, and Robert Andrews Millikan in the early 20th century. The vocational and preparatory schools were disbanded and spun off in 1910, and the college assumed its present name in 1920. In 1934, Caltech was elected to the Association of American Universities, and the antecedents of NASA's Jet Propulsion Laboratory, which Caltech continues to manage and operate, were established between 1936 and 1943 under Theodore von Kármán. Caltech has six academic divisi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bachelor's Degree
A bachelor's degree (from Medieval Latin ''baccalaureus'') or baccalaureate (from Modern Latin ''baccalaureatus'') is an undergraduate degree awarded by colleges and universities upon completion of a course of study lasting three to six years (depending on the institution and academic discipline). The two most common bachelor's degrees are the Bachelor of Arts (BA) and the Bachelor of Science (BS or BSc). In some institutions and educational systems, certain bachelor's degrees can only be taken as graduate or postgraduate educations after a first degree has been completed, although more commonly the successful completion of a bachelor's degree is a prerequisite for further courses such as a master's or a doctorate. In countries with qualifications frameworks, bachelor's degrees are normally one of the major levels in the framework (sometimes two levels where non-honours and honours bachelor's degrees are considered separately). However, some qualifications titled bachelor's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Theory
In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph theory), vertices'' (also called ''nodes'' or ''points'') which are connected by ''Glossary of graph theory terms#edge, edges'' (also called ''arcs'', ''links'' or ''lines''). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics. Definitions Definitions in graph theory vary. The following are some of the more basic ways of defining graphs and related mathematical structures. Graph In one restricted but very common sense of the term, a graph is an ordered pair G=(V,E) comprising: * V, a Set (mathematics), set of vertices (also called nodes or points); * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ihara Zeta Function
In mathematics, the Ihara zeta function is a zeta function associated with a finite graph. It closely resembles the Selberg zeta function, and is used to relate closed walks to the spectrum of the adjacency matrix. The Ihara zeta function was first defined by Yasutaka Ihara in the 1960s in the context of discrete subgroups of the two-by-two p-adic special linear group. Jean-Pierre Serre suggested in his book ''Trees'' that Ihara's original definition can be reinterpreted graph-theoretically. It was Toshikazu Sunada who put this suggestion into practice in 1985. As observed by Sunada, a regular graph is a Ramanujan graph if and only if its Ihara zeta function satisfies an analogue of the Riemann hypothesis. Definition The Ihara zeta function is defined as the analytic continuation of the infinite product :\zeta_(u)=\prod_\frac, where ''L''(''p'') is the ''length'' L(p) of p. The product in the definition is taken over all prime closed geodesics p of the graph G = (V, E), whe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Audrey Terras
Audrey Anne Terras (born September 10, 1942) is an American mathematician who works primarily in number theory. Her research has focused on quantum chaos and on various types of zeta functions. Early life and education Audrey Terras was born September 10, 1942, in Washington, D.C. She received a BS degree in mathematics from the University of Maryland, College Park (UMD) in 1964, and MA and PhD degrees from Yale University in 1966 and 1970 respectively. She was married to fellow UMD alumnus Riho Terras. She stated in a 2008 interview that she chose to study mathematics because "The U.S. government paid me! And not much! It was the time of Sputnik, so we needed to produce more mathematicians, and when I was deciding between Math and History, they weren’t paying me to do history, they were paying me to do math." Career Terras joined the University of California, San Diego, as an assistant professor in 1972, and became a full professor there in 1983. She retired in 2010, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stark's Conjecture
In number theory, the Stark conjectures, introduced by and later expanded by , give conjectural information about the coefficient of the leading term in the Taylor expansion of an Artin L-function associated with a Galois extension ''K''/''k'' of algebraic number fields. The conjectures generalize the analytic class number formula expressing the leading coefficient of the Taylor series for the Dedekind zeta function of a number field as the product of a regulator related to S-units of the field and a rational number. When ''K''/''k'' is an abelian extension and the order of vanishing of the L-function at ''s'' = 0 is one, Stark gave a refinement of his conjecture, predicting the existence of certain S-units, called Stark units, which generate abelian extensions of number fields. Formulation General case The Stark conjectures, in the most general form, predict that the leading coefficient of an Artin L-function is the product of a type of regulator, the Stark regu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
