منابع مشابه
Ternary Form Equations
Let T be a homogeneous polynomial in three variables and with rational integer coëfficients. As a generalisation of Thue’s equation we consider the ternary form equation T (x, y, z) = 1 in the integral unknowns x, y, z. We prove some general results when the degree of T is at most three and make some modest inroads into the case degT > 3. Generalisations to algebraic number fields are considere...
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 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...
متن کاملGeneration of Chaos using Ramanujans Ternary Quadratic Form
Ramanujans Ternary Quadratic Form represents a series of numbers that satisfy a tripartite quadratic relation. In the present work, we examine the sequence of numbers generated by such forms and other related forms obtained by varying the coefficients and exponents to other values. Chaotic characterization using standard techniques such as Lyapunov Exponents, Kolmogorov Entropy, Fractal Dimensi...
متن کاملAnalogue of Sylvester-cayley Formula for Invariants of Ternary Form
The number ν d (n) of linearly independed homogeneous invariants of degree n for the ternary form of degree d is calculated. The folloving formula is hold is number of nonnegative integer solutions of the system of equations
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1995
ISSN: 0022-314X
DOI: 10.1006/jnth.1995.1105