Small solutions of congruences over algebraic number fields
Let \(f_ 1({\mathfrak x}),...,f_ k({\mathfrak x})\) be homogeneous polynomials in n variables over the ring of integers R in a number field, and let A be a nonzero ideal in R. We obtain small solutions to the system of congruences \(f_ 1({\mathfrak x})\equiv \cdot \cdot \cdot \equiv f_ k({\mathfrak x})\equiv 0\) (mod A), the notion of a small point being given two interpretations, a point having coordinates with small norms, and a point having coordinates of small size. Linear systems, quadratic systems, and more general systems are all dealt with.
congruences over algebraic number fields
scientific article; zbMATH DE number 3983303