Martina Catozzi: Lattices and integer points. Diplom thesis, Ferrara 1994. Original title: Reticoli e punti interi.

LATTICES Matrices over a ring Free abelian groups Lattices and their bases Characterization of lattices as discrete subgroups Minkowski's theorem Every prime p = 1 (mod 4) is sum of two squares Every natural number is sum of four squares An algorithm for finding a vector of minimal length in a plane lattice Hermite normal form Diophantine approximation Reduction of bases in a lattice Vectors of minimal length in lattices of rank > 2 An algorithm for finding the Hermite normal form The method of genetic optimization Genetic optimization for finding a vector of minimal length in a lattice Genetic optimization for base reduction Smith normal form and the fundamental theorem for finite abelian groups INTEGER POINTS The integer part of a number Summation formulas Integer points in a plane region Van der Corput's theorem Sierpinski's theorem on integer points on a circle Integer points in region delimited by a hyperbola REFERENCES