Notes on theta series for Niemeier lattices

TL;DR

This paper provides explicit formulas for the theta series of Niemeier lattices and explores their congruence relations, contributing to the understanding of their mathematical properties.

Contribution

It introduces explicit expressions for the theta series of Niemeier lattices and examines their congruence relations, which was not previously detailed.

Findings

Explicit formulas for theta series of Niemeier lattices

Identification of congruence relations among their theta series

Enhanced understanding of lattice properties

Abstract

Some explicit expressions are given for the theta series of Niemeier lattices. As an application, we present some of their congruence relations.