On the Zeros of Eisenstein Series

descriptionPublicationkeyboard_double_arrow_right Article 01 Jul 1970 English Publisher:WileyJournal:Bulletin of the London Mathematical Society, volume 2, pages 169-170 (issn: 0024-6093,

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Authors: Rankin, F. K. C.; Swinnerton-Dyer, H. P. F.;

doi: 10.1112/blms/2.2.169

On the Zeros of Eisenstein Series

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Abstract

\textit{K. Wohlfahrt} [Math. Nachr. 26, 381--383 (1964; Zbl 0126.07703)] and \textit{R. A. Rankin} [Publ. Ramanujan Inst. 1 (1968/69), 137--144 (1969; Zbl 0198.06901)] showed that the zeros of the Eisenstein series \(E_(\tau)\) of dimension \(-k\) (for the full modular group) lie on the unit circle, or on a transform of this circle, for even \(k\leq 34\). The authors prove by simple arguments that this holds for all even \(k\).

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