Strictly regular ternary Hermitian forms

Almost power-Hermitian rings

In this paper we define a new type of rings ”almost powerhermitian rings” (a generalization of almost hermitian rings) and establish several sufficient conditions over a ring R such that, every regular matrix admits a diagonal power-reduction.

2-universal Hermitian Lattices over Imaginary Quadratic Fields

We call a positive definite integral quadratic form universal if it represents all positive integers. Then Lagrange’s Four Square Theorem means that the sum of four squares is universal. In 1930, Mordell [M] generalized this notion to a 2-universal quadratic form: a positive definite integral quadratic form that represents all binary positive definite integral quadratic forms, and showed that t...

Finiteness results for regular ternary quadratic polynomials

In 1924, Helmut Hasse established a local-to-global principle for representations of rational quadratic forms. Unfortunately, an analogous local-to-global principle does not hold for representations over the integers. A quadratic polynomial is called regular if such a principle exists; that is, if it represents all the integers which are represented locally by the polynomial itself over Zp for ...

Five regular or nearly-regular ternary quadratic forms

Witt group of Hermitian forms over a noncommutative discrete valuation ring

We investigate Hermitian forms on finitely generated torsion modules over a noncommutative discrete valuation ring. We also give some results for lattices, which still are satisfied even if the base ring is not commutative. Moreover, for a noncommutative discrete-valued division algebra D with valuation ring R and residual division algebra D̄, we prove that W(D̄) ∼=WT(R), where WT(R) denotes the ...