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The Mordell – Weil theorem was at the start of what later became a very extensive theory.
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Mordell and –
This began in his doctoral work leading to the Mordell – Weil theorem ( 1928, and shortly applied in Siegel's theorem on integral points ).
* Mordell – Weil theorem
An example of a theorem from geometric model theory is Hrushovski's proof of the Mordell – Lang conjecture for function fields.
* Case g = 1: no points, or C is an elliptic curve and its rational points form a finitely generated abelian group ( Mordell's Theorem, later generalized to the Mordell – Weil theorem ).
Because of the Mordell – Weil theorem, Faltings ' theorem can be reformulated as a statement about the intersection of a curve C with a finitely generated subgroup Γ of an abelian variety A. Generalizing by replacing C by an arbitrary subvariety of A and Γ by an arbitrary finite-rank subgroup of A leads to the Mordell – Lang conjecture, which has been proved.
* 1945 – 1953 Louis Mordell
These include the Bruck – Chowla – Ryser theorem, the Ankeny – Artin – Chowla congruence, the Chowla – Mordell theorem, and the Chowla – Selberg formula, and the Mian – Chowla sequence.
The basic result ( Mordell – Weil theorem ) says that A ( K ), the group of points on A over K, is a finitely-generated abelian group.
# proved that the average rank of the Mordell – Weil group of an elliptic curve over Q is bounded above by 7 / 6.
* Mordell – Weil theorem
In mathematics, the Chowla – Mordell theorem is a result in number theory determining cases where a Gauss sum is the square root of a prime number, multiplied by a root of unity.
# REDIRECT Mordell – Weil theorem
He made a number of conjectures in diophantine geometry: Mordell – Lang conjecture, Bombieri – Lang conjecture, Lang's integral point conjecture, Lang – Trotter conjecture, Lang conjecture on Gamma values, Lang conjecture on analytically hyperbolic varieties.
Mordell and Weil
Numerous direct calculations were done, and the proof of the Mordell – Weil theorem had to proceed by some surrogate of a finiteness proof for a particular H < sup > 1 </ sup > group.
This implies the weak Mordell – Weil theorem that its subgroup B ( K )/ f ( A ( K )) is finite.
Mordell and theorem
The general approach of diophantine geometry is illustrated by Faltings ' theorem ( a conjecture of L. J. Mordell ) starting that an algebraic curve C of genus g > 1 over the rational numbers has only finitely many rational points.
Mordell's theorem on the finite generation of the group of rational points on an elliptic curve is in Chapter 16, and integer points on the Mordell curve in Chapter 26.
Leaving aside issues of generality, and a completely different style, the major mathematical difference between the two books is that Lang used abelian varieties and offered a proof of Siegel's theorem, while Mordell noted that the proof " is of a very advanced character " ( p. 263 ).
His basic work on Mordell's theorem is from 1921 / 2, as is the formulation of the Mordell conjecture.
Mordell and was
Bull had long prepared for this event, and soon re-appeared as a professor at McGill University, which was in the process of building up a large engineering department under the direction of Donald Mordell.
In 1964 Donald Mordell was able to convince the Canadian government of the value of the HARP project as a low-cost method for Canada to enter the space-launch business, and arranged a joint Canadian-US funding program of $ 3 million a year for three years, with the Canadians supplying $ 2. 5 million of that.
The reduction of the Mordell conjecture to the Shafarevich conjecture was due to.
The Mordell conjecture for function fields was proved by and by.
A special case of the conjectures, which are open in the general case, was involved in the proof of the Mordell conjecture by Gerd Faltings.
In 1930-1960 research on the geometry of numbers was conducted by many number theorists ( including Louis Mordell, Harold Davenport and Carl Ludwig Siegel ).
The year 1938-1939 was spent in England on a Guggenheim Fellowship visiting both the University of Cambridge and the University of Manchester, meeting G. H. Hardy, John Edensor Littlewood, Harold Davenport, Kurt Mahler, Louis Mordell, and Paul Erdős.
It was proved and published independently by Sarvadaman Chowla and Louis Mordell, around 1951.
The ' if ' part was known to Gauss: the contribution of Chowla and Mordell was the ' only if ' direction.
He was awarded the Fields Medal in 1986 for proving the Mordell conjecture, which states that any non-singular projective curve of genus g > 1 defined over a number field K contains only finitely many K-rational points.
Louis Joel Mordell ( 28 January 1888 – 12 March 1972 ) was a British mathematician, known for pioneering research in number theory.
This conjecture was proved by Gerd Faltings as a step in his proof of the Mordell conjecture.
This was a novel contribution to the circle of ideas around the Mordell conjecture and abc conjecture, suggesting something of large importance to the integer solutions ( affine space ) aspect of diophantine equations.
Mordell and at
Mordell had long maintained links with CARDE and became one of Bull's ardent supporters, in spite of what other professors saw as " second-rate attempts at manipulation " and that " always supported Bull's work … I think sometimes he got pretty tired of supporting Bull.
He took an appointment at the University of Manchester in 1937, just at the time when Louis Mordell had recruited émigrés from continental Europe to build an outstanding department.
Mordell and what
Having taken third place in the Mathematical Tripos, he 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
Mordell and very
Chapman quotes Louis Mordell as saying " His result is very pretty, and there are many applications of it.
Mordell and theory
In number theory, the Mordell conjecture is the conjecture made by that a curve of genus greater than 1 over the field Q of rational numbers has only finitely many rational points.
The fields of diophantine approximation and transcendence theory have expanded, to the point that the techniques have been applied to the Mordell conjecture.
The development of Arakelov theory and its exploitation by Gerd Faltings in his proof of the Mordell conjecture is a dramatic example.
Mordell and .
Famous alumni include Nobel Laureate in nuclear physics Sir John Cockcroft, aeroplane pioneer Sir Arthur Whitten Brown, and designer of the Lancaster bomber Roy Chadwick, while famous academics include mathematicians Louis Joel Mordell, Hanna Neumann, Lewis Fry Richardson and Robin Bullough, and the physicist Henry Lipson.
* Case g > 1: according to the Mordell conjecture, now Faltings ' Theorem, C has only a finite number of rational points.
Compiled by Albert Mordell.
The structural result of Mordell, that the rational points on an elliptic curve E form a finitely-generated abelian group, used an infinite descent argument based on E / 2E in Fermat's style.
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