000			03642nam a22005415i 4500
001			978-3-319-56172-1
003			DE-He213
005			20210118125938.0
007			cr nn 008mamaa
008			170612s2017 gw | s |||| 0|eng d
020			_a9783319561721 _9978-3-319-56172-1
024	7		_a10.1007/978-3-319-56172-1 _2doi
050		4	_aQA241-247.5
072		7	_aPBH _2bicssc
072		7	_aMAT022000 _2bisacsh
072		7	_aPBH _2thema
082	0	4	_a512.7 _223
100	1		_aCooper, Shaun. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut
245	1	0	_aRamanujan's Theta Functions _h[electronic resource] / _cby Shaun Cooper.
250			_a1st ed. 2017.
264		1	_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2017.
300			_aXVIII, 687 p. 1 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_aPreface -- 0. Sum to Product Identities -- 1. Elliptic Functions -- 2. Transformations -- 3. Theta Functions -- 4. Levels 1, 2, 3, and 4: Jacobi's Inversion Theorem and Ramanujan's Alternative Theories -- 5. Level 5: The Rogers-Ramanujan Continued Fraction -- 6. Level 6: Ramanujan's Cubic Continued Fraction -- 7. Level 7 -- 8. Level 8: The Ramanujan-Gollnitz-Gordon Continued Fraction -- 9. Level 9 -- 10. Level 10: Ramanujan's Function k -- 11. Levels 11 and 23 -- 12. Level 12 -- 13. Hypergeometric Modular Transformations -- 14. Ramanujan's Series for 1/pi -- References.
520			_aTheta functions were studied extensively by Ramanujan. This book provides a systematic development of Ramanujan’s results and extends them to a general theory. The author’s treatment of the subject is comprehensive, providing a detailed study of theta functions and modular forms for levels up to 12. Aimed at advanced undergraduates, graduate students, and researchers, the organization, user-friendly presentation, and rich source of examples, lends this book to serve as a useful reference, a pedagogical tool, and a stimulus for further research. Topics, especially those discussed in the second half of the book, have been the subject of much recent research; many of which are appearing in book form for the first time. Further results are summarized in the numerous exercises at the end of each chapter.
650		0	_aNumber theory.
650		0	_aAlgebraic geometry.
650	1	4	_aNumber Theory. _0http://scigraph.springernature.com/things/product-market-codes/M25001
650	2	4	_aAlgebraic Geometry. _0http://scigraph.springernature.com/things/product-market-codes/M11019
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783319561714
776	0	8	_iPrinted edition: _z9783319561738
776	0	8	_iPrinted edition: _z9783319858432
856	4	0	_uhttps://doi.org/10.1007/978-3-319-56172-1
912			_aZDB-2-SMA
999			_c447192 _d447192
942			_cEB
506			_aAvailable to subscribing member institutions only. Доступно лише організаціям членам підписки.
506			_fOnline access from local network of NaUOA.
506			_fOnline access with authorization at https://link.springer.com/
506			_fОнлайн-доступ з локальної мережі НаУОА.
506			_fОнлайн доступ з авторизацією на https://link.springer.com/