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|a UAMI
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1 |
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|a Shidlovskiĭ, A. B.
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| 245 |
1 |
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|a Transcendental numbers /
|c Andrei Borisovich Shidlovskii ; with a foreword by W. Dale Brownawell ; translated from the Russian by Neal Koblitz.
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| 260 |
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|a Berlin :
|b W. de Gruyter,
|c 1989.
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| 300 |
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|a 1 online resource (xix, 466 pages)
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| 336 |
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|a text
|b txt
|2 rdacontent
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| 337 |
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|a computer
|b c
|2 rdamedia
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| 338 |
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|a online resource
|b cr
|2 rdacarrier
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| 347 |
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|a data file
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1 |
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|a De Gruyter studies in mathematics ;
|v 12
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0 |
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|a Foreword -- Preface to the English edition -- Preface -- Notation -- Introduction -- 1. Approximation of algebraic numbers -- 2. The classical method of Hermite-Lindemann -- 3. Methods arising from the solution of Hilbert's Seventh Problem, and their subsequent development -- 4. Siegel's method and its further development -- Chapter 1. Approximation of real and algebraic numbers -- 1. Approximation of real numbers by algebraic numbers -- 2. Simultaneous approximation -- 3. Approximation of algebraic numbers by rational numbers.
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| 505 |
8 |
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|a 4. Approximation of algebraic numbers by algebraic numbers -- 5. Further refinements and generalizations of Liouville's Theorem -- Remarks -- Chapter 2. Arithmetic properties of the values of the exponential function at algebraic points -- 1. Transcendence of e -- 2. Transcendence of s -- 3. Transcendence of the values of the exponential function at algebraic points -- 4. Approximation of ez by rational functions -- 5. Linear approximating forms for eu1z ..., eumz -- 6. A set of linear approximating forms -- 7. Lindemann's Theorem.
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| 505 |
8 |
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|a 8. Linear approximating forms and the Newton interpolation series for the exponential function -- Remarks -- Chapter 3. Transcendence and algebraic independence of the values of F-functions which are not connected by algebraic equations over the field of rational functions -- 1. E-functions -- 2. The First Fundamental Theorem -- 3. Some properties of linear and fractional-linear forms -- 4. Properties of linear forms in functions which satisfy a system of homogeneous linear differential equations -- 5. Order of zero of a linear form at z = 0.
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| 505 |
8 |
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|a 6. The determinant of a set of linear forms -- 7. Passing to linearly independent numerical linear forms -- 8. Auxiliary lemmas on solutions of systems of homogeneous linear equations -- 9. Functional linear approximating forms -- 10. Numerical linear approximating forms -- 11. Rank of the m-tuple f1(q) ..., fm(q) -- 12. Proof of the First Fundamental Theorem -- 13. Consequences of the First Fundamental Theorem -- Remarks.
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| 505 |
8 |
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|a Chapter 4. Transcendence and algebraic independence of the values of F-functions which are connected by algebraic equations over the field of rational functions -- 1. Rank of the m-tuple f1(q) ..., fm(q) -- 2. Some lemmas -- 3. Estimate for the dimension of a vector space spanned by monomials in elements of a field extension -- 4. The Third Fundamental Theorem -- 5. Transcendence of the values of F-functions connected by arbitrary algebraic equations over C(z) -- 6. Algebraic independence of the values of E-functions which are connected by arbitrary algebraic equations over C(z)
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| 504 |
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|a Includes bibliographical references.
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| 546 |
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|a English.
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| 590 |
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|a eBooks on EBSCOhost
|b EBSCO eBook Subscription Academic Collection - Worldwide
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| 650 |
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0 |
|a Transcendental numbers.
|
| 650 |
|
0 |
|a Number theory.
|
| 650 |
|
6 |
|a Nombres transcendants.
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| 650 |
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6 |
|a Théorie des nombres.
|
| 650 |
|
7 |
|a MATHEMATICS
|x Algebra
|x Intermediate.
|2 bisacsh
|
| 650 |
|
7 |
|a Number theory
|2 fast
|
| 650 |
|
7 |
|a Transcendental numbers
|2 fast
|
| 700 |
1 |
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|a Koblitz, Neal,
|d 1948-
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| 776 |
0 |
8 |
|i Print version:
|a Shidlovskii, Andrei B.
|t Transcendental Numbers.
|d Berlin/Boston : De Gruyter, ©1989
|z 9783110115680
|
| 830 |
|
0 |
|a De Gruyter studies in mathematics ;
|v 12.
|
| 856 |
4 |
0 |
|u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=558783
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