Number Theory Commons^™

The Smallest Solution Of An Isotropic Quadratic Form, Deborah H. Blevins

Theses and Dissertations--Mathematics

An isotropic quadratic form f(x₁,...,x_n) = ∑ ⁿ_i=1 ∑ ⁿ_j=1 f_ijx_ix_j defined on a Z- lattice has a smallest solution, where the size of the solution is measured using the infinity norm (∥ ∥_∞), the l₁ norm (∥ ∥₁), or the Euclidean norm (∥ ∥₂). Much work has been done to find the least upper bound and greatest lower bound on the smallest solution, beginning with Cassels in the mid-1950’s. Defining F := (f₁₁,...,f …