000			02967cam a22003617a 4500
001			18087639
003			OSt
005			20240509144548.0
008			140331t20142014nyu b 001 0 eng d
010			_a 2014936970
020			_a9781493908318 (alk. paper)
020			_a1493908316 (alk. paper)
020			_z9781493908325 (ebook)
035			_a(OCoLC)ocn871318852
040			_aYDXCP _beng _cIISERB
042			_alccopycat
050	0	0	_aQA247.5 _b.M87 2014
082			_223 _a510 M96T
100	1		_aMurty, Maruti Ram. _930095
245	1	0	_aTranscendental numbers _cM. Ram Murty, Purusottam Rath.
260			_aNew York: _bSpringer, _c2014.
300			_axiv, 217 pages ; _c24 cm
504			_aIncludes bibliographical references (pages 205-213) and index.
505	0		_a1. Liouville's theorem -- 2. Hermite's theorem -- 3. Lindemann's theorem -- 4. The Lindemann-Weierstrass theorem -- 5. The maximum modulus principle and its applications -- 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. 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 class group L-functions -- 27. Transcendence of values of modular forms -- 28. Periods, multiple zeta functions and [zeta](3).
520	3		_aThis 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 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.--
650		0	_aTranscendental numbers. _930096
650		7	_aTranscendental numbers. _2fast _930096
700	1		_aRath, Purusottam. _930097
906			_a7 _bcbc _ccopycat _d2 _eepcn _f20 _gy-gencatlg
942			_2ddc _cBK
999			_c10272 _d10272