USING KATSURADA'S DETERMINATION OF THE EISENSTEIN SERIES TO COMPUTE SIEGEL EIGENFORMS

被引：4

作者：

King, Oliver D. ^{[1
,2
]}

Poor, Cris ^{[3
]}

Shurman, Jerry ^{[4
]}

Yuen, David S. ^{[5
,6
]}

机构：

[1] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

[2] Univ Massachusetts, Med Sch, Dept Neurol, Worcester, MA 01655 USA

[3] Fordham Univ, Dept Math, Bronx, NY 10458 USA

[4] Reed Coll, Dept Math, Portland, OR 97202 USA

[5] Lake Forest Coll, Dept Math & Comp Sci, 555 N Sheridan Rd, Lake Forest, IL 60045 USA

[6] Univ Hawaii, Dept Math, 2565 McCarthy Mall, Honolulu, HI 96822 USA

来源：

MATHEMATICS OF COMPUTATION | 2018年 / 87卷 / 310期

关键词：

Eisenstein series; F-p polynomial; Siegel eigenform; SPINOR L-FUNCTION; MODULAR-FORMS; CUSP FORMS; CONJECTURE; VALUES; LIFTS;

D O I：

10.1090/mcom/3218

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We compute Hecke eigenform bases of spaces of level one, degree three Siegel modular forms and 2-Euler factors of the eigenforms through weight 22. Our method uses the Fourier coefficients of Siegel Eisenstein series, which are fully known and computationally tractable by the work of H. Katsurada; we also use P. Garrett's decomposition of the pullback of the Eisenstein series through the Witt map. Our results support I. Miyawaki's conjectural lift, and they give examples of eigenforms that are congruence neighbors.

引用

页码：879 / 892

页数：14

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