Well-Rounded Zeta-Function of Planar Arithmetic Lattices
نویسنده
چکیده
We investigate the properties of the zeta-function of well-rounded sublattices of a fixed arithmetic lattice in the plane. In particular, we show that this function has abscissa of convergence at s = 1 with a real pole of order 2, improving upon a result of [11]. We use this result to show that the number of well-rounded sublattices of a planar arithmetic lattice of index less or equal N is O(N logN) as N → ∞. To obtain these results, we produce a description of integral well-rounded sublattices of a fixed planar integral wellrounded lattice and investigate convergence properties of a zeta-function of similarity classes of such lattices, building on the results of [7].
منابع مشابه
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