Rational Reciprocity Laws
نویسنده
چکیده
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 splitting of minimal polynomials and considers ways in which this law can be extended.
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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