Analyze zeros of Eisenstein series of odd weight for congruence groups

Investigate the location, limiting geometry, and arithmetic nature of zeros of Eisenstein series of odd weights for congruence subgroups Γ, analogous to the even-weight results proved in the paper.

Background

Most of the paper’s results concern even weights, where constant terms and non-vanishing at cusps are controlled via Bernoulli polynomials and Kluyver sums. Odd weights exhibit different constant-term behavior and symmetries, and the analogous global analysis of zeros (zero-free regions, Hausdorff limits, and arithmetic) is not developed here.