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1	An integral formula for the number of lattice points in a domain Aizenberg, Lev, Tarkhanov, Nikolai January 2014 (has links) Using the multidimensional logarithmic residue we show a simple formula for the difference between the number of integer points in a bounded domain of R^n and the volume of this domain. The difference proves to be the integral of an explicit differential form over the boundary of the domain. logarithmic residue lattice point Mathematics
2	Dedekind Sums: Properties and Applications to Number Theory and Lattice Point Enumeration Meldrum, Oliver January 2019 (has links) No description available. Mathematics Dedekind Sums lattice point enumeration number theory
3	Pologrupy mřížových bodů / Semigroups of lattice points Scholle, Marek January 2012 (has links) The thesis deals with subsemigroups of (Nm 0 , +), a special discussion is later devoted to the cases m = 1, m = 2 and m = 3. We prove that a subsemigroup of Nm 0 is finitely generated if and only if its generated cone is finitely generated (equivalently polyhedral) and we describe basic topological properties of such cones. We give a few examples illustrating that conditions sufficient for finite generation in N2 0 can not be easily trans- ferred to higher dimensions. We define the Hilbert basis and the related notion of Carathéodory's rank. Besides their basic properties we prove that Carathédory's rank of a subsemigroup of Nm 0 , m = 1, 2, 3, is less than or equal to m. A particular attention is devoted to the subsemigroups containing non-trivial subsemigroups of "subtractive" elements.
4	Lattice Point Counting through Fractal Geometry and Stationary Phase for Surfaces with Vanishing Curvature Campolongo, Elizabeth Grace 02 September 2022 (has links) No description available. Mathematics Heisenberg norm Heisenberg group Heisenberg sphere vanishing curvature lattice point counting stationary phase oscillatory integrals energy integrals Hausdorff dimension Fourier transform surface measure decay fractal geometry geometric measure theory harmonic analysis Fourier analysis intersection of surfaces Gauss circle problem

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