Powers of the Dedekind eta function and the Bessenrodt-Ono inequality

In this talk I present recent results obtained with Markus Neuhauser towards the non-vanishing of the coefficients of the Dedekind eta function in the spirit of G.-C. Rota. This includes Serre’s table, pentagonal numbers, results of Kostant in the context of simple affine Lie algebras and the Lehmer conjecture. In the second part I will talk about partition numbers and the Bessenrodt-Ono inequality.