Reciprocity for jacobi sums

Charles Helou

doi:10.1006/jnth.1993.1046

Reciprocity for jacobi sums

Charles Helou

Penn State Brandywine

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Abstract

Let l be an odd prime number and p, q be two prime numbers ≡ 1 (mod l). If χ, χ′ (resp. ψ, ψ′) are multiplicative characters of order l on the finite field F_p (resp. F_q), then the corresponding Jacobi sums J(χ, χ′) and J(ψ, ψ′) satisfy the reciprocity relation [formula] where (-) denotes the lth power residue symbol over the cyclotomic field of lth roots of unity.

Original language	English (US)
Pages (from-to)	214-221
Number of pages	8
Journal	Journal of Number Theory
Volume	44
Issue number	2
DOIs	https://doi.org/10.1006/jnth.1993.1046
State	Published - 1993

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1006/jnth.1993.1046

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title = "Reciprocity for jacobi sums",

abstract = "Let l be an odd prime number and p, q be two prime numbers ≡ 1 (mod l). If χ, χ′ (resp. ψ, ψ′) are multiplicative characters of order l on the finite field Fp (resp. Fq), then the corresponding Jacobi sums J(χ, χ′) and J(ψ, ψ′) satisfy the reciprocity relation [formula] where (-) denotes the lth power residue symbol over the cyclotomic field of lth roots of unity.",

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T1 - Reciprocity for jacobi sums

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N2 - Let l be an odd prime number and p, q be two prime numbers ≡ 1 (mod l). If χ, χ′ (resp. ψ, ψ′) are multiplicative characters of order l on the finite field Fp (resp. Fq), then the corresponding Jacobi sums J(χ, χ′) and J(ψ, ψ′) satisfy the reciprocity relation [formula] where (-) denotes the lth power residue symbol over the cyclotomic field of lth roots of unity.

AB - Let l be an odd prime number and p, q be two prime numbers ≡ 1 (mod l). If χ, χ′ (resp. ψ, ψ′) are multiplicative characters of order l on the finite field Fp (resp. Fq), then the corresponding Jacobi sums J(χ, χ′) and J(ψ, ψ′) satisfy the reciprocity relation [formula] where (-) denotes the lth power residue symbol over the cyclotomic field of lth roots of unity.

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DO - 10.1006/jnth.1993.1046

M3 - Article

AN - SCOPUS:43949170988

SN - 0022-314X

VL - 44

SP - 214

EP - 221

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 2

ER -

Reciprocity for jacobi sums

Abstract

All Science Journal Classification (ASJC) codes

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