Automorphic products that are singular modulo primes

被引:0
作者
Wang, Haowu [1 ]
Williams, Brandon [2 ]
机构
[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China
[2] Rhein Westfal TH Aachen, Lehrstuhl Math A, D-52056 Aachen, Germany
关键词
THETA OPERATOR; P KERNEL; FORMS; ALGEBRAS;
D O I
10.1007/s40993-023-00495-1
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We use Rankin-Cohen brackets on O(n, 2) to prove that the Fourier coefficients of reflective Borcherds products often satisfy congruences modulo certain primes.
引用
收藏
页数:16
相关论文
共 22 条
  • [1] On the kernel of the theta operator mod p
    Boecherer, Siegfried
    Kodama, Hirotaka
    Nagaoka, Shoyu
    [J]. MANUSCRIPTA MATHEMATICA, 2018, 156 (1-2) : 149 - 169
  • [2] On mod p singular modular forms
    Boecherer, Siegfried
    Kikuta, Toshiyuki
    [J]. FORUM MATHEMATICUM, 2016, 28 (06) : 1051 - 1065
  • [3] Automorphic forms with singularities on Grassmannians
    Borcherds, RE
    [J]. INVENTIONES MATHEMATICAE, 1998, 132 (03) : 491 - 562
  • [4] AUTOMORPHIC-FORMS ON O-S+2,O-2(R) AND INFINITE PRODUCTS
    BORCHERDS, RE
    [J]. INVENTIONES MATHEMATICAE, 1995, 120 (01) : 161 - 213
  • [5] Bruinier JH, 2002, LECT NOTES MATH, V1780, P1
  • [6] Differential operators on Jacobi forms of several variables
    Choie, Y
    Kim, H
    [J]. JOURNAL OF NUMBER THEORY, 2000, 82 (01) : 140 - 163
  • [7] Automorphic forms and Lorentzian Kac-Moody algebras. Part II
    Gritsenko, VA
    Nikulin, VV
    [J]. INTERNATIONAL JOURNAL OF MATHEMATICS, 1998, 9 (02) : 201 - 275
  • [8] Gritsenko Valery A., 1996, MAT SBORNIK, V187, P27, DOI [DOI 10.4213/sm171, 10.1070/SM1996v187n11ABEH000171]
  • [9] Congruence subgroups and orthogonal groups
    Hauffe-Waschbuesch, Adrian
    Krieg, Aloys
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2021, 618 : 22 - 36
  • [10] On the theta operator for Hermitian modular forms of degree 2
    Kikuta, Toshiyuki
    Nagaoka, Shoyu
    [J]. ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG, 2017, 87 (01): : 145 - 163