Ternary quadratic forms and Shimura’s correspondence
نویسندگان
چکیده
منابع مشابه
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...
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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 ...
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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...
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We investigate the representation of integers by quadratic forms whose theta series lie in Kohnen’s plus space M 3/2(4p), where p is a prime. Conditional upon certain GRH hypotheses, we show effectively that every sufficiently large discriminant with bounded divisibility by p is represented by the form, up to local conditions. We give an algorithm for explicitly calculating the bounds. For smal...
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...
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ژورنال
عنوان ژورنال: Nagoya Mathematical Journal
سال: 1981
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s0027763000019218