Asymptotics of crank generating functions and Ramanujan congruences

Abstract

In this paper we obtain asymptotic formulas for the Fourier coefficients of an infinite family of crank generating functions. Moreover we use this result to show that the crank obeys certain inequalities. This implies that the crank can not explain any partition congruences in the usual way beside the three deduced by Ramanujan.

arXiv comment27 pages