There is a rational reciprocity law for 8th powers, due to Williams.

There are several different ways to express reciprocity laws.

On 8 April he became the first to prove the quadratic reciprocity law.

Looking at the 19th Century development of number theory we return to Gauss and his reciprocity law.

Lemmermeyer states that there has been an explosion of interest in the rational reciprocity laws since the 1970s.

As an example, there are rational biquadratic and octic reciprocity laws.

There are also quadratic reciprocity laws in rings other than the integers.

It forms the starting point in his formulation of the reciprocity law, where an important role is played by certain arithmetically defined special points.

In mathematics, an explicit reciprocity law is a formula for the Hilbert symbol of a local field.

The quadratic reciprocity law is the statement that certain patterns found in the table are true in general.

The origins of class field theory lie in the quadratic reciprocity law proved by Gauss.

The class field theory project included the 'higher reciprocity laws' (cubic reciprocity) and so on.

"Proof of the most general reciprocity law [f]or an arbitrary number field".

It is related to reciprocity laws, and can be defined in terms of the Artin symbol of local class field theory.

The reciprocity law states that, for distinct odd primes,.)

But that may not last; distributors and legislators in some of those states are working to repeal the reciprocity laws, as Maine did last year.

Therefore, the Artin reciprocity law can be interpreted as one of the main theorems of global class field theory.

Evaluation of the Legendre symbol can be achieved with the help of quadratic reciprocity law.

Despite his health, Eisenstein continued writing paper after paper on quadratic partitions of prime numbers and the reciprocity laws.

The precise correspondence between these different kinds of L-functions constitutes Artin's reciprocity law.

There are a number of equivalent ways of stating Burde's rational biquadratic reciprocity law.

There are also several explicit reciprocity laws for various generalizations of the Hilbert symbol to higher local fields, p-divisible groups, and so on.

These symbols are used in the statement and proof of cubic, quartic, Eisenstein, and related higher reciprocity laws.

In mathematics, a reciprocity law is a generalization of the law of quadratic reciprocity.

The latter dependence follows a reciprocity law, meaning that dislocations images become narrower inversely as the angular distance grows.