منابع مشابه
Kaplansky’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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Our basic problem is to answer the question : when are two quadratic forms equivalent by a rational or integral change of basis? We shall temporarily suppose that all our forms are non-degenerate (i.e., have non-zero determinant), although degenerate forms really give no trouble, The answer in the rational case is given by the celebrated HasseMinkowski theorem, which is usually stated in the form:
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Let Q be a positive definite integral quadratic form in ti variables, with the additional property that the adjoint form Q' is also integral. Using the functional equation of the Epstein zeta function, we obtain a symmetric functional equation of the ¿-function of Q with a primitive character to mod q (additive or multiplicative) defined by £io(2(x))C(x)-ï. Re(s) > nl2> where the summation exte...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1978
ISSN: 0022-314X
DOI: 10.1016/0022-314x(78)90003-3