On the kernel of the theta operator mod p

On the mod p kernel of the theta operator and Eisenstein series

“…Böcherer, Kodama and the first author argue the first method in [3]. In several cases, it gives F ∈ M k (Sp n (Z)) Z (p) with Θ(F ) ≡ 0 mod p and ω(F ) = k. As for the second method, the operator A(p) is defined by…”