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Record Nr. |
UNINA9910299989203321 |
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Autore |
Murty M. Ram |
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Titolo |
Transcendental Numbers / / by M. Ram Murty, Purusottam Rath |
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Pubbl/distr/stampa |
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New York, NY : , : Springer New York : , : Imprint : Springer, , 2014 |
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ISBN |
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Edizione |
[1st ed. 2014.] |
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Descrizione fisica |
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1 online resource (219 p.) |
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Disciplina |
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Soggetti |
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Number theory |
Algebra |
Mathematical analysis |
Number Theory |
Analysis |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references (pages [205]-213) and index. |
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Nota di contenuto |
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1. Liouville’s theorem -- 2. Hermite’s Theorem -- 3. Lindemann’s theorem -- 4. The Lindemann-Weierstrass theorem -- 5. The maximum modulus principle -- 6. Siegel’s lemma -- 7. The six exponentials theorem -- 8. Estimates for derivatives -- 9. The Schneider-Lang theorem -- 10. Elliptic functions -- 11. Transcendental values of elliptic functions -- 12. Periods and quasiperiods -- 13. Transcendental values of some elliptic integrals -- 14. The modular invariant -- 15. Transcendental values of the j-function -- 16. More elliptic integrals -- 17. Transcendental values of Eisenstein series -- 18. Elliptic integrals and hypergeometric series -- 19. Baker’s theorem -- 20. Some applications of Baker’s theorem -- 21. Schanuel’s conjecture -- 22. Transcendental values of some Dirichlet series -- 23. Proof of the Baker-Birch-Wirsing theorem -- 24. Transcendence of some infinite series -- 25. Linear independence of values of Dirichlet L-functions -- 26. Transcendence of values of modular forms -- 27. Transcendence of values of class group L-functions -- 28. Periods, multiple zeta functions and (3). . |
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Sommario/riassunto |
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This book provides an introduction to the topic of transcendental numbers for upper-level undergraduate and graduate students. The text is constructed to support a full course on the subject, including |
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descriptions of both relevant theorems and their applications. While the first part of the book focuses on introducing key concepts, the second part presents more complex material, including applications of Baker’s theorem, Schanuel’s conjecture, and Schneider’s theorem. These later chapters may be of interest to researchers interested in examining the relationship between transcendence and L-functions. Readers of this text should possess basic knowledge of complex analysis and elementary algebraic number theory. |
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