Number Theory : Proceedings of the Third Matscience Conference Held at Mysore, India, June 3-6, 1981

conducts three conferences a year, one in pure mathematics, one in theoretical physics and another on applications of mathematical methods in the garden city of Mysore or the hill resort of Ootacamund. Since 1979, in pure mathematics, in conformity with the RamanuJan tradition, it was decided to conduct annual conferences in Number Theory with the active cooperation of the number theory group at the Tata Institute of Fundamental Research~ Bombay. It was our good fortune to have had Professor Paul Erd~s as the distinguished invitee for our Third Conference on Number Theory held at Mysore during June 3-6, 1981 with Professors K.Ramachandra of the Tata Institute of Fundamental Research, R.P.Bambah of the punjab University, Chandigarh and Krishnaswami Alladi, till recently at the University of Michigan and now at MAT~CIENCE~ as the other principal lecturers. According to the established conventions of our Institute the nt~nber of participants is usually limited to about thirty to provide for one hour lectures and enough time for discussions. These proceedings comprise ten of the invited addresses and contributed papers besides problems proposed in a special session chaired by Professor Erd~s. We are grateful to all the participants for their active and enthusiastic cooperation and in particular to Professor Paul Erd~s who flew to Madras directly from Waterloo~ Canada immediately after receiving an honorary doctorate there~ to be in time for MATSCIENCE Conference. It is indeed an example of international collaboration that the Springer Verlag, through its Editor Professor Dold, is publishing these proceedings in their lecture notes series. The contributions not included in this volume are being published elsewhere. A complete list of participants and their addresses are given overleaf. Additive functions and special sets of integers....Pages 1-49 Some new problems and results in number theory....Pages 50-74 Some recent results on positive values of non-homogeneous indefinite quadratic forms....Pages 75-81 On a number of theoretical problems involved in the study of the physics of spin-systems....Pages 82-92 Order-free integers (mod m)....Pages 93-100 Perfect totient numbers....Pages 101-105 A brief summary of some results in the analytic theory of numbers-II....Pages 106-118 Addendum to my paper a brief summary of some results in the analytic theory of numbers....Pages 119-122 Some Ω-results for Ramanujan’s τ-function....Pages 123-137 On certain expoential and character sums....Pages 138-156 Partitions with congruence conditions and color restrictions....Pages 157-169 Problem session (Chaired by Prof. P. Erdös) two problems proposed by K. Ramachandra....Pages 170-177 Edited By K. Alladi. Includes Bibliographies. Includes Bibliographical References And Index.