منابع مشابه
Conjugate Algebraic Numbers Close to a Symmetric Set
A new proof is presented for the Motzkin theorem saying that if a set consists of d− 1 complex points and is symmetric relative to the real axis, then there exists a monic, irreducible, and integral polynomial of degree d whose roots are as close to each of these d−1 points as we wish. Unlike the earlier proofs, the new proof is efficient, i.e., it gives both an explicit construction of the pol...
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Let n be a positive integer. Let ξ be an algebraic real number of degree greater than n. It follows from a deep result of W. M. Schmidt that, for every positive real number ε, there are infinitely many algebraic numbers α of degree at most n such that |ξ−α| < H(α)−n−1+ε, where H(α) denotes the näıve height of α. We sharpen this result by replacing ε by a function H 7→ ε(H) that tends to zero wh...
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This is a summary of my 1994–1995 course on Algebraic Numbers. (Revised and improved on 1993– 1994!) The background assumed is standard elementary number theory—as found in my Level III course—and a little (Abelian) group theory. Corrections and suggestions for improvement are welcome, and will be credited in future editions! I first learned algebraic number theory from Stewart & Tall’s book ([...
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The roots of our subject go back to ancient Greece while its branches touch almost all aspects of contemporary mathematics. In 1801 the Disquisitiones Arithmeticae of Carl Friedrich Gauss was first published, a “founding treatise,” if ever there was one, for the modern attitude towards number theory. Many of the still unachieved aims of current research can be seen, at least in embryonic form, ...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1998
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700032408