Pseudo-normalized Hecke eigenform and its application to extremal $2$-modular lattices

arXiv (Cornell University)

Abstract

It is shown that extremal $2$-modular lattices of ranks $32$ and $48$ are generated by their vectors of minimal norm. In the proof, we use certain properties of the difference of normalized Hecke eigenforms. We refer to them as the pseudo-normalized Hecke eigenform, the concept of which is introduced in this paper.

Authors 2

1. Tsuyoshi Miezaki Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University , 52056 Aachen , Germany

2. Gabriele Nebe

   Waseda University

   Affiliation as printed

   Faculty of Science and Engineering , Waseda University , Tokyo 169-8555 , Japan