منابع مشابه
Levels of Positive Definite Ternary Quadratic Forms
The level N and squarefree character q of a positive definite ternary quadratic form are defined so that its associated modular form has level N and character Xg ■ We define ä collection of correspondences between classes of quadratic forms having the same level and different discriminants. This makes practical a method for finding representatives of all classes of ternary forms having a given ...
متن کاملRepresentations of integers by certain positive definite binary quadratic forms
We prove part of a conjecture of Borwein and Choi concerning an estimate on the square of the number of solutions to n= x2 +Ny2 for a squarefree integer N .
متن کاملPositive Definite Quadratic Forms, Elliptic Curves and Cubic Congruences
Let F (x, y) = ax + bxy + cy be a positive definite binary quadratic form with discriminant Δ whose base points lie on the line x = −1/m for an integer m ≥ 2, let p be a prime number and let Fp be a finite field. Let EF : y = ax + bx + cx be an elliptic curve over Fp and let CF : ax + bx + cx ≡ 0(mod p) be the cubic congruence corresponding to F . In this work we consider some properties of pos...
متن کاملFINITENESS THEOREMS FOR POSITIVE DEFINITE n-REGULAR QUADRATIC FORMS
An integral quadratic form f of m variables is said to be n-regular if f globally represents all quadratic forms of n variables that are represented by the genus of f . For any n ≥ 2, it is shown that up to equivalence, there are only finitely many primitive positive definite integral quadratic forms of n+3 variables that are n-regular. We also investigate similar finiteness results for almost ...
متن کامل2-universal Positive Definite Integral Quinary Quadratic Forms
As a generalization of the famous four square theorem of Lagrange, Ramanujan and Willerding found all positive definite integral quaternary quadratic forms that represent all positive integers. In this paper, we find all positive definite integral quinary quadratic forms that represent all positive definite integral binary quadratic forms. We also discuss recent results on positive definite int...
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: Acta Arithmetica
سال: 1986
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-45-4-319-328