Weber's class number problem and its variants

2022/11/28 by Hyuga Yoshizaki, Yoshizaki, Hyuga
Mathematics · #11R23 #11R27 #11R58 #14H52 #57K14 #57M12 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions #Number Theory (math.NT) #Primary 11R29 #Secondary 11E95

paper · pdf · doi:10.48550/arxiv.2211.15201

openalex publication_date 2022/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We survey Weber's class number problem and its variants in the spirit of arithmetic topology; we recollect some history, present a relation to certain units and generalized Pell's equation, and overview a study of the p-adic limits of class numbers in ℤ_p-towers together with numerical investigation for knots and elliptic curves.

Related

• The p-adic limits of class numbers in ℤ_p-towers
• Class Numbers and Pell's Equation x² + 105y² = z²
• Local torsion primes and the class numbers associated to an elliptic curve over ℚ
• Generalized Pell's equations and Weber's class number problem
• Generation of class fields by using the Weber function