First published in 1975, this classic book gives a systematic account of transcendental number theory, that is those numbers which cannot be expressed as the roots of algebraic equations having rational coefficients. Their study has developed into a fertile and extensive theory enriching many branches of pure mathematics. Expositions are presented of theories relating to linear forms in the logarithms of algebraic numbers, of Schmidt's generalization of the Thue-Siegel-Roth theorem, of Shidlovsky's work on Siegel's E-functions and of Sprindzuk's solution to the Mahler conjecture. The volume was revised in 1979, however Professor Baker has taken this further opportunity to update the book including new advances in the theory and many new references.
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A systematic account of transcendental number theory, or those numbers which cannot be expressed as the roots of algebraic equations having rational coefficients. First published in 1975 and revised in 1979.
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First Sentence:
The theory of transcendental numbers was originated by Liouville in his famous memoir of 1844 in which he obtained, for the first time, a class, tres-etendue, as it was described in the title of the paper, of numbers that satisfy no algebraic equation with integer coefficients. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
minimal defining polynomial, algebraic independence, nombres transcendants, implied constant depends, transcendence measures, transcendence theory, greatest prime factor, transcendental number theory, algebraic coefficients, transcendental numbers, algebraic numbers, imaginary quadratic fields, algebraic integers, quadratic irrational, simultaneous approximation, successive minima, constants implied, algebraic values, rational integers, abelian functions, diophantine approximation, algebraic number field, many polynomials, transcendence degree, integer divisible Key Phrases - Capitalized Phrases (CAPs): (learn more)
Acta Arith, London Math, Geometry of Numbers New!
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The theory of transcendental numbers was originated by Liouville in his famous memoir of 1844 in which he obtained, for the first time, a class, tres-etendue, as it was described in the title of the paper, of numbers that satisfy no algebraic equation with integer coefficients. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
minimal defining polynomial, algebraic independence, nombres transcendants, implied constant depends, transcendence measures, transcendence theory, greatest prime factor, transcendental number theory, algebraic coefficients, transcendental numbers, algebraic numbers, imaginary quadratic fields, algebraic integers, quadratic irrational, simultaneous approximation, successive minima, constants implied, algebraic values, rational integers, abelian functions, diophantine approximation, algebraic number field, many polynomials, transcendence degree, integer divisible Key Phrases - Capitalized Phrases (CAPs): (learn more)
Acta Arith, London Math, Geometry of Numbers New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
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- Pure Mathematics 3 & 4 (Advanced Modular Mathematics) (v. 3 & 4) by Graham Smithers in Front Matter
- A Panorama of Number Theory or The View from Baker's Garden by Gisbert Wüstholz on 5 pages
- My Numbers, My Friends by Paulo Ribenboim on 4 pages
- Pi: A Source Book by Lennart Berggren on page 619, page 640, and page 653
- Fields Medallists' Lectures (World Scientific Series in 20th Century Mathematics , Vol 5) by Micheal Atiyah on page 161, and page 192
- Internal Logic - Foundations of Mathematics from Kronecker to Hilbert (SYNTHESE LIBRARY Volume 310) by Y. Gauthier on page 189, and Back Matter
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