Transcendental numbers /:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin :
W. de Gruyter,
1989.
|
| Schriftenreihe: | De Gruyter studies in mathematics ;
12. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 1 online resource (xix, 466 pages) |
| Bibliographie: | Includes bibliographical references. |
| ISBN: | 9783110889055 3110889056 |
Internformat
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| 245 | 1 | 0 | |a Transcendental numbers / |c Andrei Borisovich Shidlovskii ; with a foreword by W. Dale Brownawell ; translated from the Russian by Neal Koblitz. |
| 260 | |a Berlin : |b W. de Gruyter, |c 1989. | ||
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| 490 | 1 | |a De Gruyter studies in mathematics ; |v 12 | |
| 505 | 0 | |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. | |
| 505 | 8 | |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. | |
| 505 | 8 | |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. | |
| 505 | 8 | |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. | |
| 505 | 8 | |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) | |
| 504 | |a Includes bibliographical references. | ||
| 546 | |a English. | ||
| 650 | 0 | |a Transcendental numbers. |0 http://id.loc.gov/authorities/subjects/sh85093223 | |
| 650 | 0 | |a Number theory. |0 http://id.loc.gov/authorities/subjects/sh85093222 | |
| 650 | 6 | |a Nombres transcendants. | |
| 650 | 6 | |a Théorie des nombres. | |
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| 650 | 7 | |a Transcendental numbers |2 fast | |
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| author | Shidlovskiĭ, A. B. |
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| contents | 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. 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. 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. 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. 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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| dewey-search | 512.73 |
| dewey-sort | 3512.73 |
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| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn815506591 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:25:01Z |
| institution | BVB |
| isbn | 9783110889055 3110889056 |
| language | English |
| oclc_num | 815506591 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xix, 466 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | W. de Gruyter, |
| record_format | marc |
| series | De Gruyter studies in mathematics ; |
| series2 | De Gruyter studies in mathematics ; |
| spelling | Shidlovskiĭ, A. B. Transcendental numbers / Andrei Borisovich Shidlovskii ; with a foreword by W. Dale Brownawell ; translated from the Russian by Neal Koblitz. Berlin : W. de Gruyter, 1989. 1 online resource (xix, 466 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier data file De Gruyter studies in mathematics ; 12 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. 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. 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. 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. 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) Includes bibliographical references. English. Transcendental numbers. http://id.loc.gov/authorities/subjects/sh85093223 Number theory. http://id.loc.gov/authorities/subjects/sh85093222 Nombres transcendants. Théorie des nombres. MATHEMATICS Algebra Intermediate. bisacsh Number theory fast Transcendental numbers fast Koblitz, Neal, 1948- http://id.loc.gov/authorities/names/n77004276 Print version: Shidlovskii, Andrei B. Transcendental Numbers. Berlin/Boston : De Gruyter, ©1989 9783110115680 De Gruyter studies in mathematics ; 12. http://id.loc.gov/authorities/names/n83742913 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=558783 Volltext |
| spellingShingle | Shidlovskiĭ, A. B. Transcendental numbers / De Gruyter studies in mathematics ; 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. 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. 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. 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. 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) Transcendental numbers. http://id.loc.gov/authorities/subjects/sh85093223 Number theory. http://id.loc.gov/authorities/subjects/sh85093222 Nombres transcendants. Théorie des nombres. MATHEMATICS Algebra Intermediate. bisacsh Number theory fast Transcendental numbers fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85093223 http://id.loc.gov/authorities/subjects/sh85093222 |
| title | Transcendental numbers / |
| title_auth | Transcendental numbers / |
| title_exact_search | Transcendental numbers / |
| title_full | Transcendental numbers / Andrei Borisovich Shidlovskii ; with a foreword by W. Dale Brownawell ; translated from the Russian by Neal Koblitz. |
| title_fullStr | Transcendental numbers / Andrei Borisovich Shidlovskii ; with a foreword by W. Dale Brownawell ; translated from the Russian by Neal Koblitz. |
| title_full_unstemmed | Transcendental numbers / Andrei Borisovich Shidlovskii ; with a foreword by W. Dale Brownawell ; translated from the Russian by Neal Koblitz. |
| title_short | Transcendental numbers / |
| title_sort | transcendental numbers |
| topic | Transcendental numbers. http://id.loc.gov/authorities/subjects/sh85093223 Number theory. http://id.loc.gov/authorities/subjects/sh85093222 Nombres transcendants. Théorie des nombres. MATHEMATICS Algebra Intermediate. bisacsh Number theory fast Transcendental numbers fast |
| topic_facet | Transcendental numbers. Number theory. Nombres transcendants. Théorie des nombres. MATHEMATICS Algebra Intermediate. Number theory Transcendental numbers |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=558783 |
| work_keys_str_mv | AT shidlovskiiab transcendentalnumbers AT koblitzneal transcendentalnumbers |