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