منابع مشابه
stability of the quadratic functional equation
In the present paper a solution of the generalizedquadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{E}$$ isgiven where $sigma$ is an involution of the normed space $E$ and$k$ is a fixed positive integer. Furthermore we investigate theHyers-Ulam-Rassias stability of the functional equation. TheHyers-Ulam stability on unbounded domains is also studied.Applic...
متن کاملRamanujan’s Ternary Quadratic Form
do not seem to obey any simple law.” Following I. Kaplansky, we call a non-negative integer N eligible for a ternary form f(x, y, z) if there are no congruence conditions prohibiting f from representing N. By the classical theory of quadratic forms, it is well known that any given genus of positive definite ternary quadratic forms represents every eligible integer. Consequently if a genus consi...
متن کاملOn almost universal ternary inhomogeneous quadratic polynomials
A fundamental question in the study of integral quadratic forms is the representation problem which asks for an effective determination of the set of integers represented by a given quadratic form. A related and equally interesting problem is the representation of integers by inhomogeneous quadratic polynomials. An inhomogeneous quadratic polynomial is a sum of a quadratic form and a linear for...
متن کاملOn 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 کاملKaplansky’s Ternary Quadratic Form
This paper proves that if N is a nonnegative eligible integer, coprime to 7, which is not of the form x2+y2+7z2, thenN is square-free. The proof is modelled on that of a similar theorem by Ono and Soundararajan, in which relations between the number of representations of an integer np2 by two quadratic forms in the same genus, the pth coefficient of an L-function of a suitable elliptic curve, a...
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ژورنال
عنوان ژورنال: Academic Journal of Applied Mathematical Sciences
سال: 2020
ISSN: 2415-2188,2415-5225
DOI: 10.32861/ajams.67.80.84