Shaked Koplewitz

The Cotype Zeta function of Z^d

I go through my work with Nathan Kaplan and Guatum Chinta, Where we give an asymptotic formula for the number of sublattices Λ ⊆ Z^d of index at most X for which Z^d /Λ has rank at most m, answering a question of Nguyen and Shparlinski. We compare this result to work of Stanley and Wang on Smith normal forms of random integral matrices and discuss connections to the Cohen-Lenstra heuristics. Our arguments are based on Petrogradsky’s formulas for the cotype zeta function of Z^d, a multivariable generalization of the subgroup growth zeta function of Z^d.