Quaternary even positive definite quadratic forms of prime discriminant

Class Numbers of Definite Quaternary Forms with Nonsquare Discriminant

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 ...

Representations 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 .

Positive 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...

FINITENESS 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 ...