The Odd Moments of Ranks and Cranks
Byungchan Kim (김병찬)
School of Liberal Arts, Seoul National University of Science and Technology, Seoul, Korea
School of Liberal Arts, Seoul National University of Science and Technology, Seoul, Korea
2012/3/28 Wed 4PM-5PM
By modifying the definition of moments of ranks and cranks, we study the odd moments of ranks and cranks. In particular, we prove the inequality between the first crank moment M1(n) and the first rank moment N1(n):
M1(n) > N1(n).
We also study new counting function ospt(n) which is equal to M1(n) – N1(n). We will also discuss higher order moments of ranks and cranks.
This is a joint work with G. E. Andrews and S. H. Chan.