A separation property of the zeros of Eisenstein series for SL(2, Z)期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	Nozaki Hiroshi

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

Abstract:	Let E_k(z) be the Eisenstein series with weight k for the modulargroup SL(2, $Z$ ). We prove that the zeros of E_k(eⁱ) interlace withthe zeros of E_k+12(eⁱ) on ${pi}$ /2 < ${theta}$ < 2 ${pi}$ /3. That is, any zeroof E_k(eⁱ) lies between two consecutive zeros of E_k+12(eⁱ) on ${pi}$ /2 < ${theta}$ < 2 ${pi}$ /3.

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