Diagonal odd-regular ternary quadratic forms

Five regular or nearly-regular ternary quadratic forms

Representation by Ternary Quadratic Forms

The problem of determining when an integral quadratic form represents every positive integer has received much attention in recent years, culminating in the 15 and 290 Theorems of Bhargava-Conway-Schneeberger and Bhargava-Hanke. For ternary quadratic forms, there are always local obstructions, but one may ask whether there are ternary quadratic forms which represent every locally represented in...

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 ...

Quadratic Forms Representing All Odd Positive Integers

We consider the problem of classifying all positive-definite integer-valued quadratic forms that represent all positive odd integers. Kaplansky considered this problem for ternary forms, giving a list of 23 candidates, and proving that 19 of those represent all positive odds. (Jagy later dealt with a 20th candidate.) Assuming that the remaining three forms represent all positive odds, we prove ...