000			03254nam a22005295i 4500
001			978-81-322-0770-2
003			DE-He213
005			20140220082928.0
007			cr nn 008mamaa
008			121009s2013 ii | s |||| 0|eng d
020			_a9788132207702 _9978-81-322-0770-2
024	7		_a10.1007/978-81-322-0770-2 _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	4	_aThe Mathematical Legacy of Srinivasa Ramanujan _h[electronic resource] / _cby M. Ram Murty, V. Kumar Murty.
264		1	_aIndia : _bSpringer India : _bImprint: Springer, _c2013.
300			_aXI, 186 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_aPreface -- Chapter 1. The Legacy of Srinivasa Ramanujan -- Chapter 2. The Ramanujan tau function -- Chapter 3. Ramanujan’s conjecture and l-adic representations -- Chapter 4. The Ramanujan conjecture from GL(2) to GL(n) -- Chapter 5. The circle method -- Chapter 6. Ramanujan and transcendence -- Chapter 7. Arithmetic of the partition function -- Chapter 8. Some nonlinear identities for divisor functions -- Chapter 9. Mock theta functions and mock modular forms -- Chapter 10. Prime numbers and highly composite numbers -- Chapter 11. Probabilistic number theory -- Chapter 12. The Sato-Tate conjecture for the Ramanujan tau-function -- Bibliography -- Index.
520			_aSrinivasa Ramanujan was a mathematician brilliant beyond compare. There is extensive literature available on the work of Ramanujan, but what is more difficult to find in the literature is an analysis that would place his mathematics in context and interpret it in terms of modern developments. The 12 lectures by G. H. Hardy, delivered in 1936, served this purpose at the time they were given. This book presents Ramanujan’s essential mathematical contributions and gives an informal account of some of the major developments that emanated from his work in the 20th and 21st centuries. It contends that his work is still having an impact on many different fields of mathematical research. The book examines some of these themes in the landscape of 21st-century mathematics. These essays, based on the lectures given by the authors, focus on a subset of Ramanujan’s significant papers and show how these papers shaped the course of modern mathematics.
650		0	_aMathematics.
650		0	_aAlgebra.
650		0	_aFourier analysis.
650		0	_aFunctions, special.
650		0	_aCombinatorics.
650		0	_aNumber theory.
650	1	4	_aMathematics.
650	2	4	_aNumber Theory.
650	2	4	_aHistory of Mathematical Sciences.
650	2	4	_aCombinatorics.
650	2	4	_aSpecial Functions.
650	2	4	_aFourier Analysis.
650	2	4	_aAlgebra.
700	1		_aMurty, V. Kumar. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9788132207696
856	4	0	_uhttp://dx.doi.org/10.1007/978-81-322-0770-2
912			_aZDB-2-SMA
999			_c99117 _d99117