Ebook: Number Theory and Discrete Mathematics

To mark the World Mathematical Year 2000 an International Conference on Number Theory and Discrete Mathematics in honour of the legendary Indian Mathematician Srinivasa Ramanuj~ was held at the centre for Advanced study in Mathematics, Panjab University, Chandigarh, India during October 2-6, 2000. This volume contains the proceedings of that conference. In all there were 82 participants including 14 overseas participants from Austria, France, Hungary, Italy, Japan, Korea, Singapore and the USA. The conference was inaugurated by Prof. K. N. Pathak, Hon. Vice-Chancellor, Panjab University, Chandigarh on October 2, 2000. Prof. Bruce C. Berndt of the University of Illinois, Urbana­ Chaimpaign, USA delivered the key note address entitled "The Life, Notebooks and Mathematical Contributions of Srinivasa Ramanujan". He described Ramanujan--as one of this century's most influential Mathematicians. Quoting Mark K. ac, Prof. George E. Andrews of the Pennsylvania State University, USA, in his message for the conference, described Ramanujan as a "magical genius". During the 5-day deliberations invited speakers gave talks on various topics in number theory and discrete mathematics. We mention here a few of them just as a sampling: • M. Waldschmidt, in his article, provides a very nice introduction to the topic of multiple poly logarithms and their special values. • C.

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Content:
Front Matter....Pages i-xvi
Multiple Polylogarithms: An Introduction....Pages 1-12
A (Conjectural) 1/3-phenomenon for the Number of Rhombus Tilings of a Hexagon which Contain a Fixed Rhombus....Pages 13-30
The Influence of Carr’s Synopsis on Ramanujan....Pages 31-35
A Bailey Lemma from the Quintuple Product....Pages 37-46
Little Flowers to G.H. Hardy(07-02-1877–01-12-1947)....Pages 47-51
Rogers-Ramanujan Type Identities for Burge’s Restricted Partition Pairs Via Restricted Frobenius Partitions....Pages 53-60
On q-additive and q-multiplicative Functions....Pages 61-76
Antimagic Labeling of Complete m-ary Trees....Pages 77-80
Some Recent Advances on Symmetric, Quasi-Symmetric and Quasi-Multiple Designs....Pages 81-88
On T-core Partitions and Quadratic Forms....Pages 89-100
Observations on Some Algebraic Equations Associated with Ramanujan’s Work....Pages 101-111
On Rapidly Convergent Series for Dirichlet L-function Values Via the Modular Relation....Pages 113-133
On a Conjecture of Andrews-II....Pages 135-147
A Note on Cordial Labelings of Multiple Shells....Pages 149-155
A Report on Additive Complements of the Squares....Pages 157-160
Transcendental Infinite Sums and Some Related Questions....Pages 161-167
The Lehmer Problem on the Euler Totient: A Pendora’s Box of Unsolvable Problems....Pages 169-178
The Problems Solved by Ramanujan in the Journal of the Indian Mathematical Society....Pages 179-187
On the gcd and lcm of Matrices Over Dedekind Domains....Pages 189-200
Hilbert’s Seventeenth Problem and Pfister’s Work on Quadratic Forms....Pages 201-211
Certain Representations of Mock-Theta Functions....Pages 213-223
Bi-Graceful Graphs....Pages 225-230
Wheels, Cages and Cubes....Pages 231-242
Relevance of Srinivasa Ramanujan at the Dawn of the New Millennium....Pages 243-249
Number of Solutions of Equations over Finite Fields and a Conjecture of Lang and Weil....Pages 251-259
On An Additive Question....Pages 261-268
....Pages 269-291