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4:00 pm Tuesday, September 12, 2017 AGNT: Counting Lattices by Cotypeby Nathan Kaplan (UC Irvine) in HBH 227- The zeta function of Z^d is a generating function that encodes the number of its sublattices of each index. This function can be expressed as a product of Riemann zeta functions and analytic properties of the Riemann zeta function then lead to an asymptotic formula for the number of sublattices of Z^d of index at most X. Nguyen and Shparlinski have investigated more refined counting questions, giving an asymptotic formula for the number of cocyclic sublattices L of Z^d, those for which Z^d/L is cyclic. Building on work of Petrogradsky, we generalize this result, counting sublattices for which Z^d/L has at most m invariant factors. We will see connections to cokernels of random integer matrices and the Cohen-Lenstra heuristics. Joint work with Gautam Chinta (CCNY) and Shaked Koplewitz (Yale).
Submitted by jb93@rice.edu |