English

Estimates on the zeros of $E_2$

Number Theory 2013-12-19 v2

Abstract

We improve the results from [EBS10] about the Eisenstein series E2(z)=124n=1nqn1qnE_2(z)=1-24\sum_{n=1}^\infty \frac{nq^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.

Cite

@article{arxiv.1312.3119,
  title  = {Estimates on the zeros of $E_2$},
  author = {Özlem Imamoglu and Jonas Jermann and Árpád Tóth},
  journal= {arXiv preprint arXiv:1312.3119},
  year   = {2013}
}

Comments

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

R2 v1 2026-06-22T02:25:21.594Z