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Bulletin of the London Mathematical Society Advance Access originally published online on March 11, 2008
Bulletin of the London Mathematical Society 2008 40(1):26-36; doi:10.1112/blms/bdm117
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© 2008 London Mathematical Society

A separation property of the zeros of Eisenstein series for SL(2, Z)

Hiroshi Nozaki

Graduate School of Mathematics
Kyushu University
Hakozaki 6-10-1
Higashi-ku
Fukuoka 812-8581
Japan

Received 4 July 2006. Revision received 16 August 2007.

Let Ek(z) be the Eisenstein series with weight k for the modular group SL(2, Z). We prove that the zeros of Ek(ei{theta}) interlace with the zeros of Ek+12(ei{theta}) on {pi}/2 < {theta} < 2{pi}/3. That is, any zero of Ek(ei{theta}) lies between two consecutive zeros of Ek+12(ei{theta}) on {pi}/2 < {theta} < 2{pi}/3.

2000 Mathematics Subject Classification 11F11 (primary), 11F03 (secondary).

Supported by a JSPS Research Fellowship.


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