2025/05/11 by Moha Ben Taleb El Hamam, Hamam, Moha Ben Taleb El
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2505.07092
openalex publication_date 2025/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \LL+=ℚ(√(2), √(pq), √(ps)) and \LL=ℚ(√(2), √(pq), √(ps), √(-ℓ)) be two fields, where q, p and s three different prime integers and ℓ≥1 be a positive odd square-free integer relatively prime to q, p and s. The purpose of this paper is to show how one can proceed to perform the calculation of unit group of the fields of the form \LL+=ℚ(√(2), √(pq), √(ps)) and \LL=ℚ(√(2), √(pq), √(ps), √(-ℓ)). More precisely, we compute the unit group and the 2-class number of these fields whenever p≡-s≡ 5\pmod 8, q≡7\pmod 8 ~~ and ~~ (( p)/( q))=(( p)/( s))=((s)/( q))=1 and (( p)/( q))=(( p)/( s)), or p≡-s≡ 5\pmod 8, q≡7\pmod 8 ~~ and ~~ (( p)/( q))=(( p)/( s))=((s)/( q))=-1.