diophantine approximation oor Sjinees

diophantine approximation

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During this time he wrote an influential paper On simultaneous Diophantine approximations on continued fractions .
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There he was influenced by Mordell to become interested in both the geometry of numbers and Diophantine approximation .
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The third chapter, the longest and most important, contains an account of Khinchin's own contributions to the topic of the metrical theory of Diophantine approximations.
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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.
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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.
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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.
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... was a landmark in the history of Diophantine approximations. It extended an idea first noted by Liouville , then pushed forward by Thue who proved that, given a rational number q and any e > 0 there are only finitely many rational numbers p /q (in their lowest terms) such that
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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.
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In 1953 the author published a book, A new method of analysis and its applications ... giving a systematic account of his methods for estimating "power sums", which he had developed (1941-53) into a versatile and powerful technique with numerous applications to Diophantine approximations, zero-free regions for the Riemann zeta function and the error term in the prime number theorem, and to problems in other parts of classical analysis.
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Approximation of algebraic numbers by rationals and applications thereof to Diophantine equations .
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