On ternary quadratic forms that represent zero
نویسندگان
چکیده
منابع مشابه
Quadratic forms that represent almost the same primes
Jagy and Kaplansky exhibited a table of 68 pairs of positive definite binary quadratic forms that represent the same odd primes and conjectured that their list is complete outside of “trivial” pairs. In this article, we confirm their conjecture, and in fact find all pairs of such forms that represent the same primes outside of a finite set.
متن کاملOn Representation Numbers of Ternary Quadratic Forms
The representation number rQ(m) is the number of integral representations of the integer m by the integral quadratic form Q over a global number field. The main obstruction to obtaining information about representation numbers is that global integrally inequevalent forms might nevertheless be equivalent over every local field (i.e. in the same genus). This failure of the localglobal principle s...
متن کاملRepresentation 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...
متن کاملFast Reduction of Ternary Quadratic Forms
We show that a positive de nite integral ternary form can be reduced with O(M(s) log s) bit operations, where s is the binary encoding length of the form and M(s) is the bit-complexity of s-bit integer multiplication. This result is achieved in two steps. First we prove that the the classical Gaussian algorithm for ternary form reduction, in the variant of Lagarias, has this worst case running ...
متن کاملGauss Sums & Representation by Ternary Quadratic Forms
This paper specifies some conditions as to when an integer m is locally represented by a positive definite diagonal integer-matrix ternary quadratic form Q at a prime p. We use quadratic Gauss sums and a version of Hensel’s Lemma to count how many solutions there are to the equivalence Q(~x) ≡ m (mod p) for any k ≥ 0. Given that m is coprime to the determinant of the Hessian matrix of Q, we can...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 1993
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089500009526