Titlebook: Number Theory IV; Transcendental Numbe A. N. Parshin,I. R. Shafarevich Book 1998 Springer-Verlag Berlin Heidelberg 1998 DEX.Slate.Transcend

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A. N. Parshin,I. R. Shafarevichr changing and fascinating field of therapeutic lipidology. Comprehensive and cutting-edge, Therapeutic Lipidology will empower readers to improve and extend the lives of the patients they so conscientiously serve..978-1-59745-533-6Series ISSN 2196-8969 Series E-ISSN 2196-8977

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0938-0396 ......................................... 11 0.1 Preliminary Remarks .................................. 11 0.2 Irrationality of J2 .............................978-3-642-08259-7978-3-662-03644-0Series ISSN 0938-0396

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,Hilbert’s Seventh Problem,dern terminology], it is with justice that they are called transcendental quantities. For this reason, logarithms are said to be transcendental.” Like Leibniz, Euler did not give a proof of his statement; in fact, it seems that nothing was published on this question before the twentieth century.

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Effective Constructions in Transcendental Number Theory,nteger coefficients that take small values at α (see §4.2). If α were rational or algebraic, there would be some polynomial .(.) ∈ ?[.], . ? 0, having α as a root. If our sequence of approximations is “dense” enough, then we can use it to eliminate α in the equation .(α) = 0, thereby obtaining a contradiction.

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978-3-642-08259-7Springer-Verlag Berlin Heidelberg 1998

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