000			03334nam a22004815i 4500
001			978-1-4939-0832-5
003			DE-He213
005			20180115171538.0
007			cr nn 008mamaa
008			140624s2014 xxu| s |||| 0|eng d
020			_a9781493908325 _9978-1-4939-0832-5
024	7		_a10.1007/978-1-4939-0832-5 _2doi
050		4	_aQA241-247.5
072		7	_aPBH _2bicssc
072		7	_aMAT022000 _2bisacsh
082	0	4	_a512.7 _223
100	1		_aMurty, M. Ram. _eauthor.
245	1	0	_aTranscendental Numbers _h[electronic resource] / _cby M. Ram Murty, Purusottam Rath.
264		1	_aNew York, NY : _bSpringer New York : _bImprint: Springer, _c2014.
300			_aXIV, 217 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_a1. 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).      .
520			_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	_aMathematics.
650		0	_aAlgebra.
650		0	_aMathematical analysis.
650		0	_aAnalysis (Mathematics).
650		0	_aNumber theory.
650	1	4	_aMathematics.
650	2	4	_aNumber Theory.
650	2	4	_aAlgebra.
650	2	4	_aAnalysis.
700	1		_aRath, Purusottam. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781493908318
856	4	0	_uhttp://dx.doi.org/10.1007/978-1-4939-0832-5
912			_aZDB-2-SMA
999			_c370878 _d370878