A weighted Möbius function

Abstract

For a fixed odd prime $\ell$, we define a variant of the classical Möbius function on the poset of isomorphism classes of finite abelian $\ell$-groups, then we prove an analog of Hall's theorem on the vanishing of the Möbius function.

7 pages, new introduction, updated references

References in corpus (3)

• Random matrices, the Cohen-Lenstra heuristics, and roots of unity
• The distribution of sandpile groups of random graphs
• Some finite abelian group theory and some q-series identities

Cited by in corpus (1)

• Random matrices, the Cohen-Lenstra heuristics, and roots of unity