Class numbers of positive definite quaternary forms

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 ...

On Zeta Functions of Orthogonal Groups of Single-class Positive Definite Quadratic Forms

Representations of Hecke–Shimura rings of integral single-class positive definite quadratic forms on relevant spaces of harmonic forms are considered, and the problem of simultaneous diagonalization of the corresponding Hecke operators is investigated. Explicit relations are deduced between zeta functions of the single-class quadratic forms in two and four variables corresponding to the harmoni...

Lectures # 7: The Class Number Formula For Positive Definite Binary Quadratic Forms

Notice that this means if we change variables ( x′ y′ ) = v′ = Av (the entries of A are integers) then Q(x′, y′) = (Av) QAv = v (A QA)v. Therefore, if Q represents a number then so does A QA. In particular, if A has an inverse with integer entries, then we get that Q and A QA represent all the same numbers. Clearly if A has an inverse B with integer entries, then det A detB = det AB = 1, thus d...

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 .