Number Theory

q-Series

 

Number theory in the spirit of Ramanujan features q-series.  The references are Number Theory in the Spirit of Ramanujan by Bruce C. Berndt,  An Introduction to q-analysis by Warren P. Johnson, and Ramanujan's Theta Functions by Shaun Cooper.

 

The q-Series articles explain and illustrate concepts, identities, and theorems for:

  1. Inversions  

  2. q-Binomial Theorems

  3. Partitions

  4. Pentagonal Numbers, Ferrer's Diagrams, and Divisors

  5. Triple and Quintuple Product Identities  

  6. Sums of Squares  

  7. Ramanujan’s Most Beautiful Identity

  8. Falls and Derangements

  9. q-Trigonometric Series