Interlacing of zeros of period polynomials

被引：0

作者：

Breland, Leanna ^{[1
]}

Le, Kevin Huu ^{[4
]}

Ni, Jingchen ^{[2
]}

O'brien, Laura ^{[5
]}

Xue, Hui ^{[3
]}

Zhu, Daozhou ^{[3
]}

机构：

[1] Mississippi State Univ, Dept Math & Stat, Mississippi State, MS 39762 USA

[2] Emory Univ, Dept Math, Atlanta, GA 30322 USA

[3] Clemson Univ, Sch Math & Stat Sci, Clemson, SC 29634 USA

[4] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

[5] Univ Calif Santa Barbara, Dept Math, Santa Barbara, CA 93106 USA

来源：

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN | 2025年 / 77卷 / 01期

关键词：

period polynomial; zeros of polynomial; interlacing between zeros; Stieltjes interlacing;

D O I：

10.2969/jmsj/92089208

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

By a lot of previous work, it is known that the zeros of the period polynomial for a newform f E s,c(ro(N)) all lie on the circle lz = 1/'N. In this paper we show that these zeros satisfy various interlacing properties for fixed N and varying k when either k or N is large. We also present a complete result when N = 1. Lastly, we establish the interlacing properties when k is fixed and N varies.

引用

页码：255 / 299

页数：45

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