منابع مشابه
Norm Euclidean Quaternionic Orders
We determine the norm Euclidean orders in a positive definite quaternion algebra over Q. Lagrange (1770) proved the four square theorem via Euler’s four square identity and a descent argument. Hurwitz [4] gave a quaternionic proof using the order Λ(2) with Z-basis: 1, i, j, 1 2 (1 + i + j + k). Here i = j = −1 and ij = −ji = k, the standard basis of the quaternions. The key property of Λ(2) is ...
متن کاملComposition and Genera of Norm-type Forms
M. Kneser has recently discovered a way to define a composition of binary quadratic forms in general [5]. His basic idea can be described as expanding the structure to include a specified action of a ring of similitudes. This approach avoids the traditional problem of "orienting" the forms, since the "proper equivalences" can be defined simply as the isometries that preserve the action of the s...
متن کاملBinary quadratic forms and Eichler orders
For any Eichler order O(D,N) of level N in an indefinite quaternion algebra of discriminant D there is a Fuchsian group Γ(D,N) ⊆ SL(2,R) and a Shimura curve X(D,N). We associate to O(D,N) a set H(O(D,N)) of binary quadratic forms which have semi-integer quadratic coefficients, and we develop a classification theory, with respect to Γ(D,N), for primitive forms contained in H(O(D,N)). In particul...
متن کاملQuadratic Polynomials Represented by Norm Forms
— Let P (t) ∈ Q[t] be an irreducible quadratic polynomial and suppose that K is a quartic extension of Q containing the roots of P (t). Let NK/Q(x) be a full norm form for the extension K/Q. We show that the variety P (t) = NK/Q(x) 6= 0 satisfies the Hasse principle and weak approximation. The proof uses analytic methods.
متن کاملLinear Forms from the Gowers Uniformity Norm
The application we have in mind is ν = p1S where S ⊆ ZN satisfies S ⊆ ZN and p = |S| /N . We do not give all the details in this note and we also assume familiarity with [1]. We sketch how to modify the argument in [1] to show the result under the assumption (1). As noted in Footnote 5 on page 16 of [1], the only hypotheses needed for the proof of the counting lemma are the strong linear forms ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1993
ISSN: 0021-8693
DOI: 10.1006/jabr.1993.1047