quadratic reciprocity law वाक्य
उदाहरण वाक्य
मोबाइल
- On 8 April he became the first to prove the quadratic reciprocity law.
- Its immense bibliography includes literature citations for 196 different published proofs for the quadratic reciprocity law.
- The latter property is called the " global reciprocity law " and is a far reaching generalization of the Gauss quadratic reciprocity law.
- In number theory, he conjectured the quadratic reciprocity law, subsequently proved by Gauss; in connection to this, the Legendre symbol is named after him.
- The Artin reciprocity law, which is a high level generalisation of the Gauss quadratic reciprocity law, states that the product vanishes on the multiplicative group of the number field.
- The description is in terms of Frobenius elements, and generalises in a far-reaching way the quadratic reciprocity law that gives full information on the decomposition of prime numbers in quadratic fields.
- Several more recent generalizations express reciprocity laws using cohomology of groups or representations of adelic groups or algebraic K-groups, and their relationship with the original quadratic reciprocity law can be hard to see.
- These laws follow easily from each version of quadratic reciprocity law stated above ( unlike with Legendre and Jacobi symbol where both the main law and the supplementary laws are needed to fully describe the quadratic reciprocity ).
- That the zeta function of a quadratic field is a product of the Riemann zeta function and a certain Dirichlet " L "-function is an analytic formulation of the quadratic reciprocity law of Gauss.
- Just as the quadratic reciprocity law for the Legendre symbol is also true for the Jacobi symbol, the requirement that the numbers be prime is not needed; it suffices that they be odd relatively prime nonunits.
- And then you can generalize this to modulo different primes, defining equivalence relations to construct Z _ p from Z, what changes if you compute modulo a number that is not a prime, etc . etc . You can probably go all the way to the proof of the quadratic reciprocity law . talk ) 13 : 27, 14 May 2013 ( UTC)
- Note that the quadratic reciprocity law allows one to easily test whether " a " is a nonzero quadratic residue mod " p ", thus we get a practical way to determine which " p "-adic numbers ( for " p " odd ) have a " p "-adic square root, and it can be extended to cover the case " p " = 2 using the more general version of Hensel's lemma ( an example with 2-adic square roots of 17 is given later ).
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