On Zeta Function of Well-rounded Lattices

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Mathematics (CMC)

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A lattice in R^n is called well-rounded (WR) if its minimal vectors with respect to Euclidean norm span R^n. This is an important class of lattices, which comes up frequently in connection with classical optimization problems. I am interested in investigating the distribution properties of WR sublattices of Z^2. For these purposes, it is important to study the behavior of some corresponding Dirichlet series, namely the determinant and minima zeta functions of WR sublattices of Z^2. In this talk I will introduce these functions, describe some of their basic analytic properties, including order of the poles, formulas and bounds for the coefficients, and product-type expressions in terms of some other well known Dirichlet series.


This lecture was given during the Analysis Seminar at the Claremont Colleges in November 2007.

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© 2007 Lenny Fukshansky

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