On theta series vanishing at ∞ and related lattices
Christine Bachoc, Riccardo Salvati Manni · Acta Arithmetica · 2006
Abstract. In this paper we consider theta series with the highest order of vanishing at the cusp ∞. When the level is a power of 2, these theta series are the m-th powers of a certain theta function with characteristic, related to the lattice √ 2 k Z m. Instead if the level is a power of 3, these theta series are the m/2-th powers of a theta series associated to the 2−dimensional root lattice A2 with characteristic. These modular forms have also many representations as theta series related to different lattices; we prove that the lattices of level a power of 2, respectively a power of 3, that afford these theta series, are lattices constructed from binary, respectively ternary codes. 1.