Polynomization of problems in Number theory related to the Dedekind eta function

For zoom details contact Pieter Moree (moree@mpim-bonn.mpg.de)

(joint work with M. Neuhauser)

In this talk I will report on recent results towards the root distribution of D'Arcais type polynomials
(the shifted Nekrasov-Okounkov polynomials). There are applications towards the Lehmer conjecture on the Ramanujan
tau-function, q-expansion of reciprocals of Eisenstein series. I will talk also on recent activities on log-concavity and the Bessenrodt-Ono
inequality of the partition function and plane partitions.