In number theory, a rational reciprocity law is a reciprocity law involving residue symbols that are related by a factor of +1 or –1 rather than a general root of unity.
As an example, there are rational biquadratic and octic reciprocity laws. Define the symbol (x|p)k to be +1 if x is a k-th power modulo the prime p and -1 otherwise.
Let p and q be distinct primes congruent to 1 modulo 4, such that (p|q)2 = (q|p)2 = +1. Let p = a2 + b2 and q = A2 + B2 with aA odd. Then
If in addition p and q are congruent to 1 modulo 8, let p = c2 + 2d2 and q = C2 + 2D2. Then
and 27 Related for: Rational reciprocity law information
In number theory, a rationalreciprocitylaw is a reciprocitylaw involving residue symbols that are related by a factor of +1 or –1 rather than a general...
In mathematics, a reciprocitylaw is a generalization of the law of quadratic reciprocity to arbitrary monic irreducible polynomials f ( x ) {\displaystyle...
quadratic reciprocity, cubic reciprocity, and quartic reciprocity. There is a rationalreciprocitylaw for 8th powers, due to Williams. Define the symbol...
In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations...
Look up reciprocity in Wiktionary, the free dictionary. Reciprocity may refer to: Reciprocity (Canadian politics), free trade with the United States of...
mathematics, an explicit reciprocitylaw is a formula for the Hilbert symbol of a local field. The name "explicit reciprocitylaw" refers to the fact that...
Lemmermeyer states that there has been an explosion of interest in the rationalreciprocitylaws since the 1970s.[A] A quartic or biquadratic residue (mod p) is...
Bounded rationality is the idea that rationality is limited when individuals make decisions, and under these limitations, rational individuals will select...
certainly rational. This concludes the proof. In the above argument, the assertion "this number is either rational or irrational" invokes the law of excluded...
K such as the fields of reals or p-adic numbers. It is related to reciprocitylaws, and can be defined in terms of the Artin symbol of local class field...
would want to be treated by them. It is sometimes called an ethics of reciprocity, meaning that you should reciprocate to others how you would like them...
In mathematics, the Weil reciprocitylaw is a result of André Weil holding in the function field K(C) of an algebraic curve C over an algebraically closed...
economic man, is the portrayal of humans as agents who are consistently rational and narrowly self-interested, and who pursue their subjectively defined...
program may be seen as Emil Artin's reciprocitylaw, which generalizes quadratic reciprocity. The Artin reciprocitylaw applies to a Galois extension of...
theory Eisenstein's reciprocitylaw is a reciprocitylaw that extends the law of quadratic reciprocity and the cubic reciprocitylaw to residues of higher...
places, i.e. equivalent over every completion of the field. Artin's reciprocitylaw implies a description of the abelianization of the absolute Galois...
Artin reciprocitylaw; in the idelic language, writing CF for the idele class group of F, and taking L to be any finite abelian extension of F, this law gives...
improving their environment through positive reciprocity (rewarding other individuals) or negative reciprocity (punishing other individuals), even in situations...
Cubic reciprocity is a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence x3 ≡ p (mod q)...
directly or indirectly, another individual, without the expectation of reciprocity or compensation for that action. Altruism can be distinguished from feelings...
provides a sense of rational autonomy, simply meaning one rationally possesses the motivation to govern their own life. Rational autonomy entails making...
is unclear, sometimes referring to reciprocity and sometimes being used as a synonym for private international law. Story distinguished it from "any absolute...
each unit takes into account at least the following elements: reciprocity, rationality, altruism (social responsibility), group gain, status, consistency...
narrowed the range of international practice that might qualify as law, favouring "rationality" over "morality" and "ethics". The 1815 Congress of Vienna marked...
that the moral law, if it exists, is universal and necessary, the only appropriate means to investigate it is through a priori rational reflection. Thus...
Artin reciprocitylaw is a general theorem in number theory that forms a central part of global class field theory. Named after Emil Artin. Ashby's law of...
ever-changing, impermanent universe (see Interdependence, Nondualism, Reciprocity). Empiricists such as Ibn Tufail in early 12th century Islamic Spain...
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