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Heath-Brown
David Rodney "Roger" Heath-Brown FRS (born 12 October 1952), is a British mathematician working in the field of analytic number theory. Education He was an undergraduate and graduate student of Trinity College, Cambridge; his research supervisor was Alan Baker. Career and research In 1979 he moved to the University of Oxford, where from 1999 he held a professorship in pure mathematics. He retired in 2016. Heath-Brown is known for many striking results. He proved that there are infinitely many prime numbers of the form ''x''3 + 2''y''3. In collaboration with S. J. Patterson in 1978 he proved the Kummer conjecture on cubic Gauss sums in its equidistribution form. He has applied Burgess's method on character sums to the ranks of elliptic curves in families. He proved that every non-singular cubic form over the rational numbers in at least ten variables represents 0. Heath-Brown also showed that Linnik's constant is less than or equal to 5.5. More recently, Heath- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kummer Sum
In mathematics, Kummer sum is the name given to certain cubic Gauss sums for a prime modulus ''p'', with ''p'' congruent to 1 modulo 3. They are named after Ernst Kummer, who made a conjecture about the statistical properties of their arguments, as complex numbers. These sums were known and used before Kummer, in the theory of cyclotomy. Definition A Kummer sum is therefore a finite sum :\sum \chi(r)e(r/p) = G(\chi) taken over ''r'' modulo ''p'', where χ is a Dirichlet character taking values in the cube roots of unity, and where ''e''(''x'') is the exponential function exp(2π''ix''). Given ''p'' of the required form, there are two such characters, together with the trivial character. The cubic exponential sum ''K''(''n'',''p'') defined by :K(n,p)=\sum_^p e(nx^3/p) is easily seen to be a linear combination of the Kummer sums. In fact it is 3''P'' where ''P'' is one of the Gaussian periods for the subgroup of index 3 in the residues mod ''p'', under multiplication, while the G ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heath-Brown–Moroz Constant
The Heath-Brown–Moroz constant ''C'', named for Roger Heath-Brown and Boris Moroz, is defined as :C=\prod_p\left(1-\frac\right)^7\left(1+\frac\right) = 0.001317641... where ''p'' runs over the primes.Finch, S. R (2003). Mathematical Constants. Cambridge, England: Cambridge University Press. Application This constant is part of an asymptotic estimate for the distribution of rational points of bounded height on the cubic surface In mathematics, a cubic surface is a surface in 3-dimensional space defined by one polynomial equation of degree 3. Cubic surfaces are fundamental examples in algebraic geometry. The theory is simplified by working in projective space rather than a ... ''X''03=''X''1''X''2''X''3. Let ''H'' be a positive real number and ''N''(''H'') the number of solutions to the equation ''X''03=''X''1''X''2''X''3 with all the ''X''''i'' non-negative integers less than or equal to ''H'' and their greatest common divisor equal to 1. Then :N(H)= C \cdot \frac + O(H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rank Of An Elliptic Curve
In mathematics, the rank of an elliptic curve is the rational Mordell–Weil rank of an elliptic curve E defined over the field of rational numbers. Mordell's theorem says the group of rational points on an elliptic curve has a finite basis. This means that for any elliptic curve there is a finite subset of the rational points on the curve, from which all further rational points may be generated. If the number of rational points on a curve is infinite then some point in a finite basis must have infinite order. The number of ''independent'' basis points with infinite order is the rank of the curve. The rank is related to several outstanding problems in number theory, most notably the Birch–Swinnerton-Dyer conjecture. It is widely believed that there is no maximum rank for an elliptic curve, and it has been shown that there exist curves with rank as large as 28, but it is widely believed that such curves are rare. Indeed, Goldfeld and later Katz– Sarnak conjectured that in a su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Berwick Prize
The Berwick Prize and Senior Berwick Prize are two prizes of the London Mathematical Society awarded in alternating years in memory of William Edward Hodgson Berwick, a previous Vice-President of the LMS. Berwick left some money to be given to the society to establish two prizes. His widow Daisy May Berwick gave the society the money and the society established the prizes, with the first Senior Berwick Prize being presented in 1946 and the first Junior Berwick Prize the following year. The prizes are awarded "in recognition of an outstanding piece of mathematical research ... published by the Society" in the eight years before the year of the award. The Berwick Prize was known as the Junior Berwick Prize up to 1999, and was given its current name for the 2001 award. Senior Berwick Prize winners Source:List of LMS prize winners ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Maynard (mathematician)
James Alexander Maynard (born 10 June 1987) is an English mathematician working in analytic number theory and in particular the theory of prime numbers. In 2017, he was appointed Research Professor at Oxford. Maynard is a fellow of St John's College, Oxford. He was awarded the Fields Medal in 2022. Biography Maynard attended King Edward VI Grammar School, Chelmsford in Chelmsford, England. After completing his bachelor's and master's degrees at Queens' College, University of Cambridge in 2009, Maynard obtained his D.Phil. from University of Oxford at Balliol College in 2013 under the supervision of Roger Heath-Brown. He then became a Fellow by Examination at Magdalen College, Oxford. For the 2013–2014 year, Maynard was a CRM-ISM postdoctoral researcher at the University of Montreal. In November 2013, Maynard gave a different proof of Yitang Zhang's theorem that there are bounded gaps between primes, and resolved a longstanding conjecture by showing that for any m there ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Senior Berwick Prize
The Berwick Prize and Senior Berwick Prize are two prizes of the London Mathematical Society awarded in alternating years in memory of William Edward Hodgson Berwick, a previous Vice-President of the LMS. Berwick left some money to be given to the society to establish two prizes. His widow Daisy May Berwick gave the society the money and the society established the prizes, with the first Senior Berwick Prize being presented in 1946 and the first Junior Berwick Prize the following year. The prizes are awarded "in recognition of an outstanding piece of mathematical research ... published by the Society" in the eight years before the year of the award. The Berwick Prize was known as the Junior Berwick Prize up to 1999, and was given its current name for the 2001 award. Senior Berwick Prize winners Source:List of LMS prize winners L ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sylvester Medal
The Sylvester Medal is a bronze medal awarded by the Royal Society (London) for the encouragement of mathematical research, and accompanied by a £1,000 prize. It was named in honour of James Joseph Sylvester, the Savilian Professor of Geometry at the University of Oxford in the 1880s, and first awarded in 1901, having been suggested by a group of Sylvester's friends (primarily Raphael Meldola) after his death in 1897. Initially awarded every three years with a prize of around £900, the Royal Society have announced that starting in 2009 it will be awarded every two years instead, and is to be aimed at 'early to mid career stage scientist' rather than an established mathematician. The award winner is chosen by the Society's A-side awards committee, which handles physical rather than biological science awards. , 45 medals have been awarded, of which all but 10 have been awarded to citizens of the United Kingdom, two to citizens of France and United States, and one medal each has be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alan Baker (mathematician)
Alan Baker (19 August 1939 – 4 February 2018) was an English mathematician, known for his work on effective methods in number theory, in particular those arising from transcendental number theory. Life Alan Baker was born in London on 19 August 1939. He attended Stratford Grammar School, East London, and his academic career started as a student of Harold Davenport, at University College London and later at Trinity College, Cambridge, where he received his PhD. He was a visiting scholar at the Institute for Advanced Study in 1970 when he was awarded the Fields Medal at the age of 31. In 1974 he was appointed Professor of Pure Mathematics at Cambridge University, a position he held until 2006 when he became an Emeritus. He was a fellow of Trinity College from 1964 until his death. His interests were in number theory, transcendence, logarithmic forms, effective methods, Diophantine geometry and Diophantine analysis. In 2012 he became a fellow of the American Mathematical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Timothy Browning
Timothy Browning is a mathematician working in number theory, examining the interface of analytic number theory and Diophantine geometry. Browning is currently a Professor of number theory at the Institute of Science and Technology Austria (ISTA) in Klosterneuburg, Austria. Awards In 2008, Browning was awarded the Whitehead Prize by the London Mathematical Society for his significant contributions on the interface of analytic number theory and arithmetic geometry concerning the number and distribution of rational and integral solutions to Diophantine equations. In 2009, Browning won the ''Ferran Sunyer i Balaguer Prize The Ferran Sunyer i Balaguer Prize is a prize in mathematics, first awarded in 1993. It honors the memory of Ferran Sunyer i Balaguer (1912–1967), a self-taught Catalan mathematician who, despite a serious physical disability, was very active ...''. The prize is awarded for a mathematical monograph of an expository nature presenting the latest developmen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Smith's Prize
The Smith's Prize was the name of each of two prizes awarded annually to two research students in mathematics and theoretical physics at the University of Cambridge from 1769. Following the reorganization in 1998, they are now awarded under the names Smith-Knight Prize and Rayleigh-Knight Prize. History The Smith Prize fund was founded by bequest of Robert Smith upon his death in 1768, having by his will left £3,500 of South Sea Company stock to the University. Every year two or more junior Bachelor of Arts students who had made the greatest progress in mathematics and natural philosophy were to be awarded a prize from the fund. The prize was awarded every year from 1769 to 1998 except 1917. From 1769 to 1885, the prize was awarded for the best performance in a series of examinations. In 1854 George Stokes included an examination question on a particular theorem that William Thomson had written to him about, which is now known as Stokes' theorem. T. W. Körner notes Only a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elliptic Curve
In mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point . An elliptic curve is defined over a field and describes points in , the Cartesian product of with itself. If the field's characteristic is different from 2 and 3, then the curve can be described as a plane algebraic curve which consists of solutions for: :y^2 = x^3 + ax + b for some coefficients and in . The curve is required to be non-singular, which means that the curve has no cusps or self-intersections. (This is equivalent to the condition , that is, being square-free in .) It is always understood that the curve is really sitting in the projective plane, with the point being the unique point at infinity. Many sources define an elliptic curve to be simply a curve given by an equation of this form. (When the coefficient field has characteristic 2 or 3, the above equation is not quite general enough to include all non-singular cubic cu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pólya Prize (LMS)
The Pólya Prize is a prize in mathematics, awarded by the London Mathematical Society. Second only to the triennial De Morgan Medal in prestige among the society's awards, it is awarded in the years that are not divisible by three – those in which the De Morgan Medal is not awarded. First given in 1987, the prize is named after Hungarian mathematician George Pólya, who was a member of the society for over 60 years. The prize is awarded "in recognition of outstanding creativity in, imaginative exposition of, or distinguished contribution to, mathematics within the United Kingdom". It cannot be given to anyone who has previously received the De Morgan Medal. List of winners * 1987 John Horton Conway * 1988 C. T. C. Wall * 1990 Graeme B. Segal * 1991 Ian G. Macdonald * 1993 David Rees * 1994 David Williams * 1996 David Edmunds * 1997 John Hammersley * 1999 Simon Donaldson * 2000 Terence Lyons * 2002 Nigel Hitchin * 2003 Angus Macintyre * 2005 Michael Berry * 2006 Peter Swin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
