|
Hans Heilbronn
Hans Arnold Heilbronn (8 October 1908 – 28 April 1975) was a mathematician. Education He was born into a German-Jewish family. He was a student at the universities of Berlin, Freiburg and Göttingen, where he met Edmund Landau, who supervised his doctorate. In his thesis, he improved a result of Hoheisel on the size of prime gaps. Life Heilbronn fled Germany for Britain in 1933 due to the rise of Nazism. He arrived in Cambridge, then found accommodation in Manchester and eventually was offered a position at Bristol University, where he stayed for about one and a half years. There he proved that the class number of the number field \mathbb(\sqrt) tends to plus infinity as d does, as well as, in collaboration with Edward Linfoot, that there are at most ten quadratic number fields of the form \mathbb(\sqrt), d a natural number, with class number 1. On invitation of Louis Mordell he moved back to Manchester Manchester () is a city in Greater Manchester, England. It had ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Berlin
Berlin ( , ) is the capital and largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's most populous city, according to population within city limits. One of Germany's sixteen constituent states, Berlin is surrounded by the State of Brandenburg and contiguous with Potsdam, Brandenburg's capital. Berlin's urban area, which has a population of around 4.5 million, is the second most populous urban area in Germany after the Ruhr. The Berlin-Brandenburg capital region has around 6.2 million inhabitants and is Germany's third-largest metropolitan region after the Rhine-Ruhr and Rhine-Main regions. Berlin straddles the banks of the Spree, which flows into the Havel (a tributary of the Elbe) in the western borough of Spandau. Among the city's main topographical features are the many lakes in the western and southeastern boroughs formed by the Spree, Havel and Dahme, the largest of which is Lake Müggelsee. Due to its l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Göttingen
Göttingen (, , ; nds, Chöttingen) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. At the end of 2019, the population was 118,911. General information The origins of Göttingen lay in a village called ''Gutingi, ''first mentioned in a document in 953 AD. The city was founded northwest of this village, between 1150 and 1200 AD, and adopted its name. In Middle Ages, medieval times the city was a member of the Hanseatic League and hence a wealthy town. Today, Göttingen is famous for its old university (''Georgia Augusta'', or University of Göttingen, "Georg-August-Universität"), which was founded in 1734 (first classes in 1737) and became the most visited university of Europe. In 1837, seven professors protested against the absolute sovereignty of the House of Hanover, kings of Kingdom of Hanover, Hanover; they lost their positions, but be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hardy-Littlewood Circle Method
A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin prime'' is used for a pair of twin primes; an alternative name for this is prime twin or prime pair. Twin primes become increasingly rare as one examines larger ranges, in keeping with the general tendency of gaps between adjacent primes to become larger as the numbers themselves get larger. However, it is unknown whether there are infinitely many twin primes (the so-called twin prime conjecture) or if there is a largest pair. The breakthrough work of Yitang Zhang in 2013, as well as work by James Maynard, Terence Tao and others, has made substantial progress towards proving that there are infinitely many twin primes, but at present this remains unsolved. Properties Usually the pair (2, 3) is not considered to be a pair of twin primes. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harold Davenport
Harold Davenport FRS (30 October 1907 – 9 June 1969) was an English mathematician, known for his extensive work in number theory. Early life Born on 30 October 1907 in Huncoat, Lancashire, Davenport was educated at Accrington Grammar School, the University of Manchester (graduating in 1927), and Trinity College, Cambridge. He became a research student of John Edensor Littlewood, working on the question of the distribution of quadratic residues. First steps in research The attack on the distribution question leads quickly to problems that are now seen to be special cases of those on local zeta-functions, for the particular case of some special hyperelliptic curves such as Y^2 = X(X-1)(X-2)\ldots (X-k). Bounds for the zeroes of the local zeta-function immediately imply bounds for sums \sum \chi(X(X-1)(X-2)\ldots (X-k)), where χ is the Legendre symbol '' modulo'' a prime number ''p'', and the sum is taken over a complete set of residues mod ''p''. In the light of this co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trinity College, Cambridge
Trinity College is a constituent college of the University of Cambridge. Founded in 1546 by Henry VIII, King Henry VIII, Trinity is one of the largest Cambridge colleges, with the largest financial endowment of any college at either Cambridge or University of Oxford, Oxford. Trinity has some of the most distinctive architecture in Cambridge with its Trinity Great Court, Great Court said to be the largest enclosed courtyard in Europe. Academically, Trinity performs exceptionally as measured by the Tompkins Table (the annual unofficial league table of Cambridge colleges), coming top from 2011 to 2017. Trinity was the top-performing college for the 2020-21 undergraduate exams, obtaining the highest percentage of good honours. Members of Trinity have been awarded 34 Nobel Prizes out of the 121 received by members of Cambridge University (the highest of any college at either Oxford or Cambridge). Members of the college have received four Fields Medals, one Turing Award and one Abel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Louis Mordell
Louis Joel Mordell (28 January 1888 – 12 March 1972) was an American-born British mathematician, known for pioneering research in number theory. He was born in Philadelphia, United States, in a Jewish family of Lithuanian extraction. Education Mordell was educated at the University of Cambridge where he completed the Cambridge Mathematical Tripos as a student of St John's College, Cambridge, starting in 1906 after successfully passing the scholarship examination. He graduated as third wrangler in 1909. Research After graduating Mordell began independent research into particular diophantine equations: the question of integer points on the cubic curve, and special case of what is now called a Thue equation, the Mordell equation :''y''2 = ''x''3 + ''k''. He took an appointment at Birkbeck College, London in 1913. During World War I he was involved in war work, but also produced one of his major results, proving in 1917 the multiplicative property of Srinivasa Ramanujan's tau- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edward Linfoot
Edward Hubert Linfoot (8 June 1905 – 14 October 1982) was a British mathematician, primarily known for his work on optics, but also noted for his work in pure mathematics. Early life and career Edward Linfoot was born in Sheffield, England, in 1905. He was the eldest child of George Edward Linfoot, a violinist and mathematician, and George's wife Laura, née Clayton. After attending King Edward VII School he won a scholarship to Balliol College at the University of Oxford. During his time at Oxford he met the number theorist G. H. Hardy, and after graduating in 1926, Linfoot completed a D.Phil under the supervision of Hardy with a thesis entitled ''Applications of the Theory of Functions of a Complex Variable''. After brief stints at the University of Göttingen, Princeton University, and Balliol College, Linfoot took a job in 1932 as assistant lecturer, and later lecturer, at the University of Bristol. During the 1930s Linfoot's interests slowly made the transition f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Field
In mathematics, an algebraic number field (or simply number field) is an extension field K of the field of rational numbers such that the field extension K / \mathbb has finite degree (and hence is an algebraic field extension). Thus K is a field that contains \mathbb and has finite dimension when considered as a vector space over The study of algebraic number fields, and, more generally, of algebraic extensions of the field of rational numbers, is the central topic of algebraic number theory. This study reveals hidden structures behind usual rational numbers, by using algebraic methods. Definition Prerequisites The notion of algebraic number field relies on the concept of a field. A field consists of a set of elements together with two operations, namely addition, and multiplication, and some distributivity assumptions. A prominent example of a field is the field of rational numbers, commonly denoted together with its usual operations of addition and multiplication. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Class Number (number Theory)
In number theory, the ideal class group (or class group) of an algebraic number field is the quotient group where is the group of fractional ideals of the ring of integers of , and is its subgroup of principal ideals. The class group is a measure of the extent to which unique factorization fails in the ring of integers of . The order of the group, which is finite, is called the class number of . The theory extends to Dedekind domains and their field of fractions, for which the multiplicative properties are intimately tied to the structure of the class group. For example, the class group of a Dedekind domain is trivial if and only if the ring is a unique factorization domain. History and origin of the ideal class group Ideal class groups (or, rather, what were effectively ideal class groups) were studied some time before the idea of an ideal was formulated. These groups appeared in the theory of quadratic forms: in the case of binary integral quadratic forms, as put into s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bristol University
, mottoeng = earningpromotes one's innate power (from Horace, ''Ode 4.4'') , established = 1595 – Merchant Venturers School1876 – University College, Bristol1909 – received royal charter , type = Public red brick research university , endowment = £91.3 million (2021) , budget = £752.0 million (2020–21) , chancellor = Paul Nurse , vice_chancellor = Professor Evelyn Welch , head_label = Visitor , head = Rt Hon. Penny Mordaunt MP , academic_staff = 3,385 (2020) , students = () , undergrad = () , postgrad = () , city = Bristol , country = England , coor = , campus = Urban , free_label = Students' Union , free = University of Bristol Union , colours = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Manchester
Manchester () is a city in Greater Manchester, England. It had a population of 552,000 in 2021. It is bordered by the Cheshire Plain to the south, the Pennines to the north and east, and the neighbouring city of Salford to the west. The two cities and the surrounding towns form one of the United Kingdom's most populous conurbations, the Greater Manchester Built-up Area, which has a population of 2.87 million. The history of Manchester began with the civilian settlement associated with the Roman fort ('' castra'') of ''Mamucium'' or ''Mancunium'', established in about AD 79 on a sandstone bluff near the confluence of the rivers Medlock and Irwell. Historically part of Lancashire, areas of Cheshire south of the River Mersey were incorporated into Manchester in the 20th century, including Wythenshawe in 1931. Throughout the Middle Ages Manchester remained a manorial township, but began to expand "at an astonishing rate" around the turn of the 19th century. Manchest ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge
Cambridge ( ) is a university city and the county town in Cambridgeshire, England. It is located on the River Cam approximately north of London. As of the 2021 United Kingdom census, the population of Cambridge was 145,700. Cambridge became an important trading centre during the Roman and Viking ages, and there is archaeological evidence of settlement in the area as early as the Bronze Age. The first town charters were granted in the 12th century, although modern city status was not officially conferred until 1951. The city is most famous as the home of the University of Cambridge, which was founded in 1209 and consistently ranks among the best universities in the world. The buildings of the university include King's College Chapel, Cavendish Laboratory, and the Cambridge University Library, one of the largest legal deposit libraries in the world. The city's skyline is dominated by several college buildings, along with the spire of the Our Lady and the English Martyrs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
