2022/12/19 by Loïc Grenié, Grenié, Loïc, Giuseppe Molteni +1
Mathematics · #11R04 #11R29 #11Y40 #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2212.09461
openalex publication_date 2022/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let K be a field of degree n and discriminant with absolute value Δ. Under the assumption of the validity of the Generalized Riemann Hypothesis, we provide a new algorithm to compute a set of generators of the class group of K and prove that the norm of the ideals in that set is ≤ (4-1/(2n))log2Δ, except for a finite number of fields of degree n≤ 4. For those fields, the conclusion holds with the slightly larger limit (4-1/(2n)+1/(2n2))log2Δ. When the cardinality of \mathcal C ℓ is odd the bounds improve to (4-2/(3n))log2Δ, again with finitely many exceptions in degree n≤ 4, and to (4-2/(3n)+3/(8n2))log2Δ without exceptions.