Five regular or nearly-regular ternary quadratic forms

Five regular or nearly-regular ternary quadratic forms

Strictly regular ternary Hermitian forms

Article history: Received 28 October 2015 Received in revised form 8 April 2016 Accepted 9 April 2016 Communicated by David Goss MSC: primary 11E39 secondary 11E12, 11E20

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 ...

DEFINITE REGULAR QUADRATIC FORMS OVER F q [ T ]

Let q be a power of an odd prime, and Fq[T ] be the ring of polynomials over a finite field Fq of q elements. A quadratic form f over Fq [T ] is said to be regular if f globally represents all polynomials that are represented by the genus of f . In this paper, we study definite regular quadratic forms over Fq [T ]. It is shown that for a fixed q, there are only finitely many equivalence classes...

FINITENESS THEOREMS FOR POSITIVE DEFINITE n-REGULAR QUADRATIC FORMS

An integral quadratic form f of m variables is said to be n-regular if f globally represents all quadratic forms of n variables that are represented by the genus of f . For any n ≥ 2, it is shown that up to equivalence, there are only finitely many primitive positive definite integral quadratic forms of n+3 variables that are n-regular. We also investigate similar finiteness results for almost ...