On Certain Ternary Cubic-Form Equations
نویسندگان
چکیده
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...
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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...
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We study trace codes with defining set L, a subgroup of the multiplicative group of an extension of degree m of the alphabet ring F3+uF3+u 2 F3, with u 3 = 1. These codes are abelian, and their ternary images are quasi-cyclic of co-index three (a.k.a. cubic codes). Their Lee weight distributions are computed by using Gauss sums. These codes have three nonzero weights when m is singly-even and |...
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ژورنال
عنوان ژورنال: American Journal of Mathematics
سال: 1880
ISSN: 0002-9327
DOI: 10.2307/2369443