000			02361nam a22002057a 4500
003			OSt
005			20240910154252.0
008			190117b ||||| |||| 00| 0 eng d
020			_a9781493976270
040			_cTata Book House _aICTS-TIFR
050			_aQA29.R3
100			_aAndrews, George E.
245			_aRamanujan's lost notebook _b: Part IV
260			_aUSA: _bSpringer, _c[c2005]
300			_a439 p
505			_aIntroduction 1. Double Series of Bessel Functions and the Circle and Divisor Problems 2. Koshliakov’s Formula and Guinand’s Formula 3. Theorems Featuring the Gamma Function 4. Hypergeometric Series 5. Two Partial Manuscripts on Euler’s Constant γ 6. Problems in Diophantine Approximation 7. Number Theory 8. Divisor Sums 9. Identities Related to the Riemann Zeta Function and Periodic Zeta Functions 10. Two Partial Unpublished Manuscripts on Sums Involving Primes 11. An Unpublished Manuscript of Ramanujan on Infinite Series Identities 12. A Partial Manuscript on Fourier and Laplace Transforms 13. Integral Analogues of Theta Functions and Gauss Sums 14. Integral Analogues of Theta Functions and Gauss Sums 15. Functional Equations for Products of Mellin Transforms 16. A Preliminary Version of Ramanujan’s Paper 17. A Preliminary Version of Ramanujan’s Paper 18. A Partial Manuscript Connected with Ramanujan’s Paper “Some Definite Integrals” 19. Miscellaneous Results in Analysis3 20. Elementary Results 21. A Strange, Enigmatic Partial Manuscript
520			_aThis 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 analysisand 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.
700			_aBerndt, Bruce C.
942			_2lcc _cBK
999			_c2144 _d2144