The present volume is the third of the series Resonance of Ramanujan`s Mathematics written by the author. The first two volumes were published in 1996. As in the first two volumes, this volume contains five chapters. The topics selected for this volume are Continued fractions-comprising of the first three chapters, Riemann Zeta function and the fifth chapter is a masterly and an up-to-date article on Elliptic Functions on alternative bases by Prof. S. Bhargava (Mysore), reprinted from the Proc. Nat. Acad. Sci (India) 68 (1998), by the kind permission of the Chief Editor. The chapters on Continued fractions, a topic in which Ramanujan has been, probably, at his best, are aimed at giving the most recent developments in that topic and should prove useful to the research workers in a better understanding of Ramanujans work and in further extending his results. The fourth chapter on Riemann Zeta function, which is of importance in the theory of numbers, asymptotic theory, and series transformations etc., gives an idea of the diverse nature of topics in which Ramanujan has made valuable contribution.
The last chapter reprinted from the Proc. Nat. Acad. Sci. (India) 68 (1998) gives an up-to-date and thorough discussion of Elliptic Function Theory on alternative bases.
This volume should prove to be a valuable asset for researchers working on Ramanujan`s Mathematics. Each chapter, as before, is followed by an up-to-date and comprehensive bibliography and provides an independent reading.
About the Author(s):
Dr. R.P. Agarwal graduated from University of Lucknow. He has been awarded Ph.D. degrees of University of Lucknow and University of London. Dr. Agarwal joined University of Lucknow as lecturer and superannuated as Professor of Pure Mathematics. He has also served as Vice-Chancellor, University of Lucknow and University of Rajasthan, Jaipur. Dr. Agarwal was also emeritus scientist, Council of Scientific and Industrial Research and Department of Science and Technology, Government of India. His specialization in the field of Integral transforms, Special Functions and Generalized Hyper-geometric Series.
Dr. Agarwal has published more than 50 research papers, and supervised Ph.D. and D.Scs of more than twenty students. He is an author of several undergraduate textbooks and a monograph on Generalised Hypergeometric Series. He has been associated with many academic activities as President and Editor of different Mathematical Associations and Societies. Dr.Agarwal is currently, Editor of the Journal of Indian Mathematical Society .
The chapters on Continued Fractions a topic in which Ramanujan has been probably at his best, presents contemporary and recent developments in the area and should prove useful to the research worker for a better understanding of Ramanujan`s work and in further extending his results. The fourth chapter on Riemann zeta function which is important in the theory of numbers, asympotic theory, and series transformations etc., gives an idea of the diverse nature of topics in which Ramanujan has made valuable contribution.