The Conway-Sloane calculus for 2-adic lattices

Abstract

We motivate and explain the system introduced by Conway and Sloane for working with quadratic forms over the 2adic integers, and prove its validity. Their system is far better for actual calculations than earlier methods, and has been used for many years, but no proof has been published before now.

Nonfreeness of algebras of symmetric Hilbert modular forms of even weight for $\mathbb{Q}(\sqrt{d})$ where d>5

“…The idea of the proof is the following. We find the lower bound for the left hand side of formula (1) and an upper bound for the right hand side. Since the l.h.s.…”

“…We need to check the equivalence over Z 2 . The algorithm for doing it can be found in [5] and [1]. There are 2 possibilities:…”