Reciprocity Laws

Lemmermeyer, F. (2000). Reciprocity Laws: From Euler to Eisenstein. Springer.

Type

Book

Intellectual base

Review or monograph

Year

2000

DOI

10.1007/978-3-662-12893-0

ISBN

9783642086281

Link

https://doi.org/10.1007/978-3-662-12893-0

Cited by

3 citations across 3 artifacts.

Domain-specific

• Eisenstein reciprocity
  • … field, integer ring and root of unity, primary convention, coprime elements and modulus restrictions, residue-symbol definition, reciprocity equation and supplementary cases are explicit. to An applied instance preserves the same invariant under changed notation, scale, jurisdiction, dataset, or implementation..
• Gauss's lemma (number theory)
  • … directly demonstrates that odd prime, coprime integer, least-positive or signed residue convention, half-system, upper-half count, Legendre symbol, and parity conclusion are explicit. to An applied instance preserves the same invariant under a changed scale, notation, jurisdiction, dataset, or implementation..
• Quartic reciprocity
  • To decide whether a is a fourth power modulo a suitable prime p, compute or transform the quartic residue character rather than enumerate every x. The character's value certifies solvability only after p and a meet coprimality and normalization requirements.

Verification

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