Arithmetic of arithmetic Coxeter groups

• DOI: 10.1073/pnas.1809537115
• Publication Date: 2018-12-27T00:45:13Z
• Authors: Suzana Milea; Christopher D. Sh...; Martin H. Weissman
• Keywords: Arithmetic progression

In the 1990s, J. H. Conway published a combinatorial-geometric method for analyzing integer-valued binary quadratic forms (BQFs). Using visualization he named "topograph," revisited reduction of BQFs and solution Diophantine equations such as Pell's equation. It appears that crux his is coincidence between arithmetic group [Formula: see text] Coxeter type There are many groups, each may have unforeseen applications to arithmetic. We introduce Conway's topograph generalizations other groups. This includes study "arithmetic flags" variants forms.