The class numbers of positive definite quadratic forms
نویسندگان
چکیده
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 ...
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Notice that this means if we change variables ( x′ y′ ) = v′ = Av (the entries of A are integers) then Q(x′, y′) = (Av) QAv = v (A QA)v. Therefore, if Q represents a number then so does A QA. In particular, if A has an inverse with integer entries, then we get that Q and A QA represent all the same numbers. Clearly if A has an inverse B with integer entries, then det A detB = det AB = 1, thus d...
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Let F (x, y) = ax + bxy + cy be a positive definite binary quadratic form with discriminant Δ whose base points lie on the line x = −1/m for an integer m ≥ 2, let p be a prime number and let Fp be a finite field. Let EF : y = ax + bx + cx be an elliptic curve over Fp and let CF : ax + bx + cx ≡ 0(mod p) be the cubic congruence corresponding to F . In this work we consider some properties of pos...
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ژورنال
عنوان ژورنال: Japanese journal of mathematics. New series
سال: 1977
ISSN: 0289-2316,1861-3624
DOI: 10.4099/math1924.3.239