A Borcherds Product in S2(K(587))−

(Filename: BP-2-587-1-1-1-hi.html)

DEFINITION OF ψ AND BORCH(ψ)
The weakly holomorphic Jacobi form ψ of weight 0 and index 587, is defined as
    ψ = (φ|V2)/φ − Θ/φ
where φ ∈ J2,587cusp, with ν(φ) = 2, is the theta block
     φ = TB(2;1,1,2,2,2,3,3,4,4,5,5,6,6,7,8,8,9,10,11,12,13,14)
= 122332425262718291101111121131141
= η(τ)4(θ(τ,z)/η(τ))2(θ(τ,2z)/η(τ))3(θ(τ,3z)/η(τ))2(θ(τ,4z)/η(τ))2(θ(τ,5z)/η(τ))2(θ(τ,6z)/η(τ))2(θ(τ,7z)/η(τ))(θ(τ,8z)/η(τ))2(θ(τ,9z)/η(τ))(θ(τ,10z)/η(τ))(θ(τ,11z)/η(τ))(θ(τ,12z)/η(τ))(θ(τ,13z)/η(τ))(θ(τ,14z)/η(τ))
and Θ ∈ J2,2·587cusp, with ν(Θ) = 2, is an inflation of φ defined by
     Θ = TB(2;1,2,2,3,3,4,4,5,6,6,7,8,9,10,10,12,13,14,15,16,18,22)
= 112232425162718191102121131141151161181221
= η(τ)4(θ(τ,z)/η(τ))(θ(τ,2z)/η(τ))2(θ(τ,3z)/η(τ))2(θ(τ,4z)/η(τ))2(θ(τ,5z)/η(τ))(θ(τ,6z)/η(τ))2(θ(τ,7z)/η(τ))(θ(τ,8z)/η(τ))(θ(τ,9z)/η(τ))(θ(τ,10z)/η(τ))2(θ(τ,12z)/η(τ))(θ(τ,13z)/η(τ))(θ(τ,14z)/η(τ))(θ(τ,15z)/η(τ))(θ(τ,16z)/η(τ))(θ(τ,18z)/η(τ))(θ(τ,22z)/η(τ))
Note that BORCH(ψ) has leading Jacobi coefficient φ given above,and so BORCH(ψ) begins with Jacobi coefficient #1.

PROPERTIES OF ψ AND BORCH(ψ)
See this page for properties of ψ and BORCH(ψ), such as Humbert divisors of BORCH(ψ) and some Fourier coefficients of BORCH(ψ).