Eksempler på brug af Geometry of numbers på Engelsk og deres oversættelser til Dansk
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Geometry of numbers and its applications to algebraic number theory.
Then in 1959 he published another book,An introduction to the geometry of numbers.
At this time Davenport worked mainly on the geometry of numbers and on Diophantine approximation;
The mathematical topics that Delone studied include algebra, the geometry of numbers.
Blichfeldt wrote papers on the geometry of numbers and he has an important book Finite Collineation Groups.
His early work was on number theory andhe wrote on Diophantine inequalities and the geometry of numbers.
His most original achievement, however, was his'geometry of numbers' which he initiated in 1890.
He had broad interests,working on mathematical economics as well as group theory and the geometry of numbers.
In Hlawka looks at Blichfeldt's contributions to the geometry of numbers, in particular looking at Blichfeldt's principle.
He may, without doubt, be called a leading scholar in the splendid andimportant field of geometry of numbers.
Davenport worked on number theory,in particular the geometry of numbers, Diophantine approximation and the analytic theory of numbers. .
Later Voronoy worked on the theory of numbers, in particular he worked on algebraic numbers and the geometry of numbers.
Together with Davenport and Mahler,Mordell initiated great advances in the geometry of numbers while he held the Chair of Pure Mathematics at Manchester.
This lecture is particularly interesting,for it contains the first example of the method which Minkowski would develop some years later in his famous"geometry of numbers.
There he was influenced by Mordell to become interested in both the geometry of numbers and Diophantine approximation.
At this time Davenport worked mainly on the geometry of numbers and on Diophantine approximation; he also acquired a lasting interest in problems of packing and covering.
Zassenhaus worked on a broad range of topics and, in addition to those mentioned above, he worked on nearfields, the theory of orders,representation theory, the geometry of numbers and the history of mathematics.
During the decade 1939-49 he wrote a series of papers dealing with the geometry of numbers, in particular dealing with Minkowski 's inequality for convex bodies.
Delone 's interests in the geometry of numbers and the structure of crystals soon began to attract Aleksandrov at least as much as his work in physics which was supervised by V A Fok.
The different approaches to this and related conjectures(and theorems) involve analytic number theory, the theory of Lie groups and algebraic groups, ergodic theory, representation theory,reduction theory, geometry of numbers and some other topics.
It gave an elementary account of his work on the geometry of numbers and of its applications to the theories of Diophantine approximation and of algebraic numbers. .
These topics are: prime numbers; congruences and the quadratic reciprocity law; continued fractions; irrational, algebraic and transcendental numbers; quadratic fields; arithmetical functions, their order of magnitude and the Dirichlet or power series which generate them; partitions and representations of numbers as sums of squares, cubes and higher powers;Diophantine approximation; and the geometry of numbers.
Work on the geometry of numbers led on to work on convex bodies and to questions about packing problems, the ways in which figures of a given shape can be placed within another given figure.
His mathematical publications started in about 1947 with a series of papers on the geometry of numbers, in particular papers on theorems of Khinchin and of Davenport, and on a problem of Mahler.
His most original achievement, however,was his'geometry of numbers' which he initiated in 1890. Geometrie der Zahlen was first published in 1910 but the first 240 pages(of the 256) appeared as the first section in 1896. Geometrie der Zahlen was reprinted in 1953 by Chelsea, New York, and reprinted again in 1968. Minkowski published Diophantische Approximationen: Eine Einführung in die Zahlentheorie in 1907.
Some of the many topics that he covered were diophantine approximations, orders of linear homogeneous groups,theory of geometry of numbers, approximate solutions of the integers of a set of linear equations, low-velocity fire angle, finite collineation groups, and characteristic roots.
In 1930, while still only 18 years of age, he began original work on optics in the Optics Institute. However Aleksandrov was taught mathematics in the Faculty of Physics by B N Delone.Delone 's interests in the geometry of numbers and the structure of crystals soon began to attract Aleksandrov at least as much as his work in physics which was supervised by V A Fok.
Other major themes of his work were p-adic numbers, p-adic Diophantine approximation, geometry of numbers(a term coined by Minkowski to describe the mathematics of packings and coverings) and measure on polynomials.
Study became a leader in the geometry of complex numbers.
With Corrado Segre,Study was one of the leading pioneers in the geometry of complex numbers.