Representation by ternary quadratic Sample Clauses

Representation by ternary quadratic forms It is a classical problem to classify the integers represented by a positive definite, integral quadratic form. In particular, one may ask when such a form represents all positive integers. This is now known due to recent theorems of Xxxxxx-Xxxxxxxxxxxx-Xxxxxxxx [9] and Xxxxxxxx-Xxxxx [8], a pair of results known as the 15 and 290 theorems. If a form does not represent all positive integers, perhaps the next best thing would be for it to represent all integers which are locally represented (represented modulo m for all integers m). Such forms are known as regular quadratic forms, and Jagy, Xxxxxxxxx, and Xxxxxxxxx [47] proved that there are at most 913 regular ternary quadratic forms, of which 899 are known to be regular. Adapting techniques of Xxx and Xxxxxxxxxxxxx [65], we prove the following theorem in Section 4.4.
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