Non-homogeneous ternary quadratic forms

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

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...

متن کامل

Fast 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 کامل

Gauss 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 کامل

Representations of Integers by Ternary Quadratic Forms

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 کامل

On 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 کامل

ذخیره 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: Acta Mathematica

سال: 1948

ISSN: 0001-5962

DOI: 10.1007/bf02393646