On Zeta-function of Well-rounded Lattices in the Plane
One powerful method of determining the asymptotic behavior of a sequence is based on studying the analytic properties of its Dirichlet-series generating function, and then applying a certain Tauberian theorem. I will start by discussing this general principle and some of its applications in algebra and number theory. I will then concentrate on the particular problem of estimating the number of fixed-index well- rounded sublattices of a given planar lattice as the index goes to infinity. This problem has recently received some attention, and I will review the known results and will show how the analytic method described above yields a desired asymptotic formula.
© 2012 Lenny Fukshansky
Fukshansky, Lenny. "On Zeta-function of Well-rounded Lattices in the Plane." Analysis Seminar, Claremont Colleges, Claremont, California. February 2012.
This lecture or seminar talk was given during an Analysis Seminar at the Claremont Colleges in February 2012.
This lecture is related to another lecture by the same author: "On Zeta Function of Well-rounded Lattices" given during an Analysis Seminar at the Claremont Colleges in November 2007.