Narrow Results

For a positive integer m, let R be either the ring ℤ_2m of integers modulo 2m or the quaternionic ring Σ_2m = ℤ_2m + αℤ_2m + βℤ_2m + γℤ_2m with α = 1 + î, β = 1 + ĵ and , where are elements of the ring ℍ of real quaternions satisfying , , and . In this paper, we obtain Jacobi forms (or Siegel modular forms) of genus r from byte weight enumerators (or symmetrized byte weight enumerators) in genus r of Type I and Type II codes over R. Furthermore, we derive a functional equation for partial Epstein zeta functions, which are summands of classical Epstein zeta functions associated with quadratic forms.

In this paper, we study holomorphic $\mathbb{Z}$-graded vertex superalgebras. We prove that all such vertex superalgebras of central charge $8$ and $16$ are purely even. For the case of central charge $24$ we prove that the weight-one Lie superalgebra is either zero, of superdimension $24$, or else is one of an explicit list of 1332 semisimple Lie superalgebras.