Abstract
In this opening chapter, brief summaries are provided for most of the following chapters. We also cite and thank the many mathematicians who have helped us in the preparation of this book.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
H. Alzer, On Ramanujan’s double inequality for the gamma function, Bull. London Math. Soc. 35 (2003), 601–607.
G.E. Andrews and B.C. Berndt, Ramanujan’s Lost Notebook, Part I, Springer, New York, 2005.
G.E. Andrews and B.C. Berndt, Ramanujan’s Lost Notebook, Part III, Springer, New York, 2012.
B.C. Berndt, Ramanujan’s Notebooks, Part II, Springer-Verlag, New York, 1989.
B.C. Berndt, An unpublished manuscript of Ramanujan on infinite series identities, J. Ramanujan Math. Soc. 19 (2004), 57–74.
B.C. Berndt and D.C. Bowman, Ramanujan’s short unpublished manuscript on integrals and series related to Euler’s constant, in Constructive, Experimental and Nonlinear Analysis, M. Thera, ed., American Mathematical Society, Providence, RI, 2000, pp. 19–27.
B.C. Berndt, H.H. Chan, and Y. Tanigawa, Two Dirichlet series evaluations found on page 196 of Ramanujan’s lost notebook, Math. Proc. Cambridge Philos. Soc. 153 (2012), 341–360.
B.C. Berndt and W. Chu, Two entries on bilateral hypergeometric series in Ramanujan’s lost notebook, Proc. Amer. Math. Soc. 135 (2007), 129–134.
B.C. Berndt and T. Huber, A fragment on Euler’s constant in Ramanujan’s lost notebook, South East Asian J. Math. and Math. Sci. 6 (2008), 17–22.
B.C. Berndt and S. Kim, A problem in diophantine approximation found in Ramanujan’s lost notebook, Ramanujan J., to appear.
B.C. Berndt, S. Kim, and A. Zaharescu, Weighted divisor sums and Bessel function series, II, Adv. Math. 229 (2012), 2055–2097.
B.C. Berndt, S. Kim, and A. Zaharescu, Circle and divisor problems, and double series of Bessel functions, Adv. Math. 236 (2013), 24–59.
B.C. Berndt, S. Kim, and A. Zaharescu, Diophantine approximation of the exponential function and Sondow’s conjecture, Adv. Math., to appear.
B.C. Berndt and P. Pongsriiam, Discarded fragments from Ramanujan’s papers, in Analytic and Probabilistic Methods in Number Theory: Kubilius Memorial Volume, Proceedings of the Fifth International Conference in Honour of J. Kubilius, Palanga, Lithuania, 4–10 September 2011, A. Laurinčikas, E. Manstavičius, and G. Stepanauskas, eds., TEV, Vilnius, 2012, pp. 49–59.
B.C. Berndt and D. Schultz, On sums of powers in Ramanujan’s lost notebook, Applic. Anal. 90 (2011), 725–730.
B.C. Berndt and P. Xu, An integral analogue of theta functions and Gauss sums in Ramanujan’s lost notebook, Math. Proc. Cambridge Philos. Soc. 147 (2009), 257–265.
B.C. Berndt and A. Zaharescu, Weighted divisor sums and Bessel function series, Math. Ann. 335 (2006), 249–283.
A. Dixit, Analogues of a transformation formula of Ramanujan, Internat. J. Number Thy. 7 (2011), 1151–1172.
A. Dixit, Analogues of the general theta transformation formula, Proc. Royal Soc. Edinburgh, Sect. A 143 (2013), 371–399.
J.H. Han and M.D. Hirschhorn, Another look at an amazing identity of Ramanujan, Math. Magazine 79 (2006), 302–304.
M.D. Hirschhorn, An amazing identity of Ramanujan, Math. Magazine 68 (1995), 199–201.
M.D. Hirschhorn, Ramanujan and Fermat’s last theorem, Austral. Math. Soc. Gaz. 31 (2004), 256–257.
S.-Y. Kang, S.-G. Lim, and J. Sohn, The continuous symmetric Hahn polynomials found in Ramanujan’s lost notebook, J. Math. Anal. Appl. 307 (2005), 153–166.
E.A. Karatsuba, On the asymptotic representation of the Euler gamma function by Ramanujan, J. Comp. Appl. Math. 135 (2001), 225–240.
S. Ramanujan, Some definite integrals connected with Gauss’s sums, Mess. Math. 44 (1915), 75–85.
S. Ramanujan, Some definite integrals, J. Indian Math. Soc. 11 (1915), 81–87.
S. Ramanujan, Question 754, J. Indian Math. Soc. 8 (1916), 80; solutions in 12 (1920), 101; 13 (1921), 151.
S. Ramanujan, Some formulae in the analytic theory of numbers, Mess. Math. 45 (1916), 81–84.
S. Ramanujan, On certain trigonometric sums and their applications in the theory of numbers, Trans. Cambridge Philos. Soc. 22 (1918), 259–276.
S. Ramanujan, Collected Papers, Cambridge University Press, Cambridge, 1927; reprinted by Chelsea, New York, 1962; reprinted by the American Mathematical Society, Providence, RI, 2000.
S. Ramanujan, Notebooks (2 volumes), Tata Institute of Fundamental Research, Bombay, 1957; second ed, 2012.
S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa, New Delhi, 1988.
L.G. Sathe, On a problem of Hardy on the distribution of integers having a given number of prime factors. I, J. Indian Math. Soc. 17 (1953), 63–82.
L.G. Sathe, On a problem of Hardy on the distribution of integers having a given number of prime factors. IV, J. Indian Math. Soc. 18 (1954), 43–81.
A. Selberg, Note on a paper by L.G. Sathe, J. Indian Math. Soc. 18 (1954), 83–87.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media New York
About this chapter
Cite this chapter
Andrews, G.E., Berndt, B.C. (2013). Introduction. In: Ramanujan's Lost Notebook. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4081-9_1
Download citation
DOI: https://doi.org/10.1007/978-1-4614-4081-9_1
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-4080-2
Online ISBN: 978-1-4614-4081-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)