Title Ramanujan's lost notebook. Part IV / George E. Andrews, Bruce C. Berndt

Published New York : Springer, ©2013

Click on the following:
Springer eBooks
Springer Mathematics and Statistics eBooks

Copies

Description 1 online resource (xvii, 439 pages) : illustrations Contents 880-01 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. Two partial manuscripts on Euler's constant y -- 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 Two partial unpublished manuscripts on sums involving primes -- 12. An unpublished manuscript of Ramanujan on infinite series identities -- 13. A partial manuscript on Fourier and Laplace transforms -- 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 "On the product [mathematical equation]" -- 17. A preliminary version of Ramanujan's paper "On the integral [mathematical equation]" -- 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 880-01/(S Introduction -- Double Series of Bessel Functions and the Circle and Divisor Problems -- Koshliakov's Formula and Guinand's Formula -- Theorems Featuring the Gamma Function -- Hypergeometric Series -- Two Partial Manuscripts on Euler's Constant γ -- Problems in Diophantine Approximation -- Number Theory -- Divisor Sums -- Identities Related to the Riemann Zeta Function and Periodic Zeta Functions -- Two Partial Unpublished Manuscripts on Sums Involving Primes -- An Unpublished Manuscript of Ramanujan on Infinite Series Identities -- A Partial Manuscript on Fourier and Laplace Transforms -- Integral Analogues of Theta Functions and Gauss Sums -- Functional Equations for Products of Mellin Transforms -- A Preliminary Version of Ramanujan's Paper "On the Product πn=0[infinity][1+(xa+nd)3] " -- A Preliminary Version of Ramanujan's Paper "On the Integral [integral]x0tan-1ttdt " -- A Partial Manuscript Connected with Ramanujan's Paper "Some Definite Integrals" -- Miscellaneous Results in Analysis -- Elementary Results -- A Strange, Enigmatic Partial Manuscript Summary "In 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."--Publisher's description Analysis Global analysis (Mathematics) Fourier analysis Functions, special Number theory Analysis Special Functions Bibliography Includes bibliographical references (pages 421-434) and index Notes English Online resource; title from PDF title page (SpringerLink, viewed November 7, 2013) Subject Ramanujan Aiyangar, Srinivasa, 1887-1920. SUBJECT Ramanujan Aiyangar, Srinivasa, 1887-1920 fast Subject Mathematical analysis. Number theory. Mathematicians -- India -- Biography Mathematics. Mathematics BIOGRAPHY & AUTOBIOGRAPHY -- Science & Technology. MATHEMATICS -- Essays. MATHEMATICS -- Pre-Calculus. MATHEMATICS -- Reference. Análisis matemático Matemáticos -- Biografías -- India Matemáticas Números , Teoría de Mathematics Mathematical analysis Mathematicians Number theory SUBJECT India Subject India Genre/Form Biographies Biographies. Biographies. Form Electronic book Author Berndt, Bruce C., 1939- ISBN 9781461440819 1461440815 1461440807 9781461440802 1322332711 9781322332710

  Permalink