Estimates on the zeros of $E_2$

Abstract

We improve the results from [EBS10] about the Eisenstein series $E_2(z)=1-24{\sum }_{n=1}^{\infty }\frac{n{q}^n}{1-q^n}$. In particular we show that there exists exactly one (simple) zero in each Ford circle and give an approximation to its location.

arXiv commentCorrected error in numerical estimates, revised references, minor improvements, results essentially unchanged