The cotype zeta function of ${\mathbb{Z}}^d$

Gautam Chinta, Nathan Kaplan, Shaked Koplewitz

We give an asymptotic formula for the number of sublattices $\Lambda \subseteq {\mathbb{Z}}^d$ of index at most $X$ for which ${\mathbb{Z}}^d/\Lambda$ has rank at most $m$, answering a question of…