On the Minimum of a Positive Definite Quadratic Form over Non--Zero Lattice points. Theory and Applications

Faustin Adiceam, Evgeniy Zorin

Let ${\Sigma }_d^{++}$ be the set of positive definite matrices with determinant 1 in dimension $d\ge 2$. Identifying any two $S{L}_d(\mathbb{Z})$-congruent elements in ${\Sigma }_d^{++}$ gives rise…