On theta series vanishing at infinity and related lattices

Christine Bachoc (1) , Riccardo Salvati Manni (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 Sapienza University of Rome - Dipartimento di Matematica "Guido Castelnuovo" [Roma I]

We consider theta series with the highest possible order of vanishing at infinity when the level is a power of 2 or 3 and the lattices associated to these theta series. We prove that these lattices are constructed from binary, respectively ternary codes.

Domaines: Théorie des nombres [math.NT]

Christine Bachoc, Riccardo Salvati Manni. On theta series vanishing at infinity and related lattices. Acta Arithmetica, 2006, 124 (1), pp.59-71. ⟨hal-00196181⟩