Kyushu Journal of Mathematics
Online ISSN : 1883-2032
Print ISSN : 1340-6116
ISSN-L : 1340-6116
INTERLACING OF ZEROS OF EISENSTEIN SERIES
Trevor GRIFFIN, Nathan KENSHUR, Abigail PRICE, Bradshaw VANDENBERG-DAVES, Hui XUE, Daozhou ZHU
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Keywords: zeros of modular forms, Eisenstein series, interlacing
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2021 Volume 75 Issue 2 Pages 249-272

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Abstract

Let Ek (z) be the normalized Eisenstein series of weight k for the full modular group SL(2, ℤ). Let a > 0 be an even integer. In this paper we completely determine when the zeros of Ek interlace with the zeros of Ek+a. This generalizes a result of Nozaki on the interlacing of zeros of Ek and Ek+12.

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