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 M

_{1}(n) and the first rank moment N_{1}(n):M

_{1}(n) > N_{1}(n).We also study new counting function ospt(n) which is equal to M_{1}(n) – N_{1}(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.

Tags: 김병찬