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 کاملPositive Definite and Semi-definite Splitting Methods for Non-hermitian Positive Definite Linear Systems
In this paper, we further generalize the technique for constructing the normal (or positive definite) and skew-Hermitian splitting iteration method for solving large sparse nonHermitian positive definite system of linear equations. By introducing a new splitting, we establish a class of efficient iteration methods, called positive definite and semi-definite splitting (PPS) methods, and prove th...
متن کاملThe Gelfand transform, positive linear functionals, and positive-definite functions
In this note, unless we say otherwise every vector space or algebra we speak about is over C. If A is a Banach algebra and e ∈ A satisfies xe = x and ex = x for all x ∈ A, and also ‖e‖ = 1, we say that e is unity and that A is unital. If A is a unital Banach algebra and x ∈ A, the spectrum of x is the set σ(x) of those λ ∈ C for which λe−x is not invertible. It is a fact that if A is a unital B...
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 کاملThe First Nontrivial Genus of Positive Definite Ternary Forms
The first nontrivial genus of positive ternary forms has discriminant 7. The paper presents all known results concerning this genus, including some computations.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1984
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1984-0746096-x