منابع مشابه
Rational Quartic Reciprocity
In 1985, K. S. Williams, K. Hardy and C. Friesen [11] published a reciprocity formula that comprised all known rational quartic reciprocity laws. Their proof consisted in a long and complicated manipulation of Jacobi symbols and was subsequently simplified (and generalized) by R. Evans [3]. In this note we give a proof of their reciprocity law which is not only considerably shorter but also she...
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for every prime p ≡ 1 mod 4 such that (p/pj) = +1 for all 1 ≤ j ≤ r. This is ’the extension to composite values of m’ that was referred to in [3], to which this paper is an addition. Here I will fill in the details of a proof, on the one hand because I was requested to do so, and on the other hand because this general law can be used to derive general versions of Burde’s and Scholz’s reciprocit...
متن کاملRational Reciprocity Laws
The purpose of this note is to provide an overview of Rational Reciprocity (and in particular, of Scholz’s reciprocity law) for the non-number theorist. In the first part, we will describe the background in number theory that will be necessary for a complete understanding of the material to be discussed in the second part. The second part focuses on a proof of Scholz’s reciprocity law using the...
متن کاملRational Points on Quartic Hypersurfaces
Let X be a projective non-singular quartic hypersurface of dimension 39 or more, which is defined over Q. We show that X(Q) is non-empty provided that X(R) is non-empty and X has p-adic points for every prime p.
متن کاملRational points on diagonal quartic surfaces
We searched up to height 107 for rational points on diagonal quartic surfaces. The computations fill several gaps in earlier lists computed by Pinch, Swinnerton-Dyer, and Bright.
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1994
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-67-4-387-390