The Kronecker symbol extends the Jacobi symbol, itself a generalization of the Legendre symbol, to all integers as its lower argument, including negative numbers, even numbers and zero. It preserves the multiplicative properties that make the Legendre and Jacobi symbols useful for determining quadratic residues, while removing the restriction that the lower argument be an odd positive integer. Named after Leopold Kronecker, the symbol is used in class field theory and in efficient algorithms for testing quadratic residuosity, and it appears in the definition of certain L-functions in algebraic number theory.
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Origin Yearintroduced by Leopold Kronecker (1885) Connections
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Source Kronecker Symbol (Wikipedia)
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Source Kronecker Symbol (Wikipedia)
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1. Kronecker Symbol (Wikipedia)
Lead section
In number theory, the Kronecker symbol, written as ( a n) {\displaystyle \left({\frac {a}{n}}\right)} or ( a | n) {\displaystyle (a|n)}, is a generalization of the Jacobi symbol to all integers n {\displaystyle n}. It was introduced by Leopold Kronecker (1885, page 770).
- In Branch: Number Theory, Lead sentence
Attributed To: Leopold Kronecker, Lead paragraph
In number theory, the Kronecker symbol, written as
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