Number Theory and Discrete Mathematics

Front Matter....Pages i-xiv
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
n-Colour Partitions....Pages 269-291
....Pages 293-299