2008/07/29 by Nils-Peter Skoruppa, Skoruppa, Nils-Peter
Mathematics · #11F11 #11F27 #11F33 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F11 #msc:11F27 #msc:11F33
paper · pdf · doi:10.48550/arxiv.0807.4694
Correction of several typos
openalex publication_date 2008/07/29 · arxiv created 2008/10/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is proved that the theta series of an even lattice whose level is a power of a prime ℓ is congruent modulo ℓ to an elliptic modular form of level~1. The proof uses arithmetic and algebraic properties of lattices rather than methods from the theory of modular forms. The methods presented here may therefore be especially pleasing to those working in the theory of quadratic forms, and they admit generalizations to more general types of theta series as they occur e.g. in the theory of Siegel or Hilbert modular forms.