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001 978-1-4614-4081-9
003 DE-He213
005 20160302170646.0
007 cr nn 008mamaa
008 130604s2013 xxu| s |||| 0|eng d
020 _a9781461440819
_9978-1-4614-4081-9
024 7 _a10.1007/978-1-4614-4081-9
_2doi
050 4 _aQA241-247.5
072 7 _aPBH
_2bicssc
072 7 _aMAT022000
_2bisacsh
082 0 4 _a512.7
_223
100 1 _aAndrews, George E.
_eauthor.
245 1 0 _aRamanujan's Lost Notebook
_h[electronic resource] :
_bPart IV /
_cby George E. Andrews, Bruce C. Berndt.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2013.
300 _aXVII, 439 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aPreface -- 1 Introduction.- 2 Double Series of Bessel Functions and the Circle and Divisor Problems.- 3 Koshliakov's Formula and Guinand's Formula.- 4 Theorems Featuring the Gamma Function.- 5 Hypergeometric Series.- 6 Euler's Constant.- 7 Problems in Diophantine Approximation.- 8 Number Theory.- 9 Divisor Sums -- 10 Identities Related to the Riemann Zeta Function and Periodic Zeta Functions -- 11 Two Partial Unpublished Manuscripts on Sums Involving Primes.- 12 Infinite Series -- 13 A Partial Manuscript on Fourier and Laplace Transforms -- 14 Integral Analogues of Theta Functions adn Gauss Sums -- 15 Functional Equations for Products of Mellin Transforms -- 16 Infinite Products -- 17 A Preliminary Version of Ramanujan's Paper, On the Integral ∫_0^x tan^(-1)t)/t dt -- 18 A Partial Manuscript Connected with Ramanujan's Paper, Some Definite Integrals.- 19 Miscellaneous Results in Analysis -- 20 Elementary Results -- 21 A Strange, Enigmatic Partial Manuscript.-  Location Guide -- Provenance -- References -- Index.
520 _aIn the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the handwriting of Srinivasa Ramanujan. This manuscript was soon designated, "Ramanujan's lost notebook." Its discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony. This volume is the fourth of five volumes that the authors plan to write on Ramanujan’s lost notebook.  In contrast to the first three books on Ramanujan's Lost Notebook, the fourth book does not focus on q-series.  Most of the entries examined in this volume fall under the purviews of number theory and classical analysis.  Several incomplete manuscripts of Ramanujan published by Narosa with the lost notebook are discussed.  Three of the partial manuscripts are on diophantine approximation, and others are in classical Fourier analysis and prime number theory.   Most of the entries in number theory fall under the umbrella of classical analytic number theory.   Perhaps the most intriguing entries are connected with the classical, unsolved circle and divisor problems. Review from the second volume: "Fans of Ramanujan's mathematics are sure to be delighted by this book. While some of the content is taken directly from published papers, most chapters contain new material and some previously published proofs have been improved. Many entries are just begging for further study and will undoubtedly be inspiring research for decades to come. The next installment in this series is eagerly awaited." - MathSciNet Review from the first volume: "Andrews and Berndt are to be congratulated on the job they are doing. This is the first step...on the way to an understanding of the work of the genius Ramanujan. It should act as an inspiration to future generations of mathematicians to tackle a job that will never be complete." - Gazette of the Australian Mathematical Society.
650 0 _aMathematics.
650 0 _aMathematical analysis.
650 0 _aAnalysis (Mathematics).
650 0 _aFourier analysis.
650 0 _aSpecial functions.
650 0 _aNumber theory.
650 1 4 _aMathematics.
650 2 4 _aNumber Theory.
650 2 4 _aAnalysis.
650 2 4 _aFourier Analysis.
650 2 4 _aSpecial Functions.
700 1 _aBerndt, Bruce C.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781461440802
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4614-4081-9
912 _aZDB-2-SMA
999 _c196533
_d196533