Invariants, seminvariants, and covariants of the ternary and quaternary quadratic form modulo 2
نویسندگان
چکیده
منابع مشابه
Ramanujan’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...
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There is a relationship between the covariants of binary forms, a central topic in classical invariant theory, and the invariants of modular representations of cyclic groups of prime order. This relationship was identified by Gert Almkvist [1] and used implicitly in both [15] and [17]. In this note we investigate the relationship and provide a progress report on an application. Our primary moti...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1915
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1915-02591-7