David Masser (Switzerland Universitat Basel)
Auxiliary Polynomials in Number Theory
David Masser (Switzerland Universitat Basel)
Auxiliary Polynomials in Number Theory
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A unified account of a powerful classical method, illustrated by applications in number theory. Aimed at graduates and professionals.
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A unified account of a powerful classical method, illustrated by applications in number theory. Aimed at graduates and professionals.
Produktdetails
- Produktdetails
- Cambridge Tracts in Mathematics
- Verlag: Cambridge University Press
- Seitenzahl: 368
- Erscheinungstermin: 21. Juni 2016
- Englisch
- Abmessung: 235mm x 157mm x 26mm
- Gewicht: 704g
- ISBN-13: 9781107061576
- ISBN-10: 1107061571
- Artikelnr.: 44694424
- Cambridge Tracts in Mathematics
- Verlag: Cambridge University Press
- Seitenzahl: 368
- Erscheinungstermin: 21. Juni 2016
- Englisch
- Abmessung: 235mm x 157mm x 26mm
- Gewicht: 704g
- ISBN-13: 9781107061576
- ISBN-10: 1107061571
- Artikelnr.: 44694424
David Masser is Emeritus Professor in the Department of Mathematics and Computer Science at the University of Basel, Switzerland. He started his career with Alan Baker, which gave him a grounding in modern transcendence theory and began his fascination with the method of auxiliary polynomials. His subsequent interest in applying the method to areas outside transcendence, which involved mainly problems of zero estimates, culminated in his works with Gisbert Wüstholz on isogeny and polarization estimates for abelian varieties, for which he was elected a Fellow of the Royal Society in 2005. This expertise proved beneficial in his more recent works with Umberto Zannier on problems of unlikely intersections, where zero estimates make a return appearance.
Introduction
1. Prologue
2. Irrationality I
3. Irrationality II - Mahler's method
4. Diophantine equations - Runge's method
5. Irreducibility
6. Elliptic curves - Stepanov's method
7. Exponential sums
8. Irrationality measures I - Mahler
9. Integer-valued entire functions I - Pólya
10. Integer-valued entire functions II - Gramain
11. Transcendence I - Mahler
12. Irrationality measures II - Thue
13. Transcendence II - Hermite-Lindemann
14. Heights
15. Equidistribution - Bilu
16. Height lower bounds - Dobrowolski
17. Height upper bounds
18. Counting - Bombieri-Pila
19. Transcendence III - Gelfond-Schneider-Lang
20. Elliptic functions
21. Modular functions
22. Algebraic independence
Appendix: Néron's square root
References
Index.
1. Prologue
2. Irrationality I
3. Irrationality II - Mahler's method
4. Diophantine equations - Runge's method
5. Irreducibility
6. Elliptic curves - Stepanov's method
7. Exponential sums
8. Irrationality measures I - Mahler
9. Integer-valued entire functions I - Pólya
10. Integer-valued entire functions II - Gramain
11. Transcendence I - Mahler
12. Irrationality measures II - Thue
13. Transcendence II - Hermite-Lindemann
14. Heights
15. Equidistribution - Bilu
16. Height lower bounds - Dobrowolski
17. Height upper bounds
18. Counting - Bombieri-Pila
19. Transcendence III - Gelfond-Schneider-Lang
20. Elliptic functions
21. Modular functions
22. Algebraic independence
Appendix: Néron's square root
References
Index.
Introduction
1. Prologue
2. Irrationality I
3. Irrationality II - Mahler's method
4. Diophantine equations - Runge's method
5. Irreducibility
6. Elliptic curves - Stepanov's method
7. Exponential sums
8. Irrationality measures I - Mahler
9. Integer-valued entire functions I - Pólya
10. Integer-valued entire functions II - Gramain
11. Transcendence I - Mahler
12. Irrationality measures II - Thue
13. Transcendence II - Hermite-Lindemann
14. Heights
15. Equidistribution - Bilu
16. Height lower bounds - Dobrowolski
17. Height upper bounds
18. Counting - Bombieri-Pila
19. Transcendence III - Gelfond-Schneider-Lang
20. Elliptic functions
21. Modular functions
22. Algebraic independence
Appendix: Néron's square root
References
Index.
1. Prologue
2. Irrationality I
3. Irrationality II - Mahler's method
4. Diophantine equations - Runge's method
5. Irreducibility
6. Elliptic curves - Stepanov's method
7. Exponential sums
8. Irrationality measures I - Mahler
9. Integer-valued entire functions I - Pólya
10. Integer-valued entire functions II - Gramain
11. Transcendence I - Mahler
12. Irrationality measures II - Thue
13. Transcendence II - Hermite-Lindemann
14. Heights
15. Equidistribution - Bilu
16. Height lower bounds - Dobrowolski
17. Height upper bounds
18. Counting - Bombieri-Pila
19. Transcendence III - Gelfond-Schneider-Lang
20. Elliptic functions
21. Modular functions
22. Algebraic independence
Appendix: Néron's square root
References
Index.