Counting lattices by cotype

09/05/2017 - 12:15pm
09/05/2017 - 1:10pm
Nathan Kaplan (UC Irvine)

The zeta function of Z^d is a generating function that encodes the number of sublattices of index k for each k. 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. This is joint work with Gautam Chinta (CCNY) and Shaked Koplewitz (Yale).

Millikan 2099, Pomona College
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There will be a short organizational meeting in the same room right before the talk at 12:00 noon.

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