On class groups of imaginary quadratic fields

DOI10.1112/jlms/jdv031zbMath1387.11080OpenAlexW2271348202WikidataQ116141800 ScholiaQ116141800MaRDI QIDQ3195124

Andrew Wiles

Publication date: 21 October 2015

Published in: Journal of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://ora.ox.ac.uk/objects/uuid:120f2970-8027-4bc5-bd93-b72a7fbc91ff

zbMATH Keywords

imaginary quadratic fieldsclass groups

Mathematics Subject Classification ID

Quadratic extensions (11R11) Galois representations (11F80) Class numbers, class groups, discriminants (11R29)

Related Items

Indivisibility of class numbers of imaginary quadratic fields, Class numbers, cyclic simple groups, and arithmetic, Two-step nilpotent extensions are not anabelian, The mean number of 3-torsion elements in ray class groups of quadratic fields, Indivisibility of relative class numbers of totally imaginary quadratic extensions and vanishing of these relative Iwasawa invariants, Odd degree number fields with odd class number, Multi-quadratic \(p\)-rational number fields, Class number divisibility for imaginary quadratic fields, Congruences of Hurwitz class numbers on square classes, A note on rank one quadratic twists of elliptic curves and the non-degeneracy of 𝑝-adic regulators at Eisenstein primes

Cites Work

• On the Davenport-Heilbronn theorems and second order terms
• Trace formulae and imaginary quadratic fields
• On ordinary \(\lambda\)-adic representations associated to modular forms
• Proof of the existence of infinitely many imaginary quadratic fields whose class number is not divisible by 3
• Modular elliptic curves and Fermat's Last Theorem
• Canonical periods and congruence formulae
• Nonvanishing modulo \(l\) of Fourier coefficients of half-integral weight modular forms
• Automorphic forms on GL (2)
• Mass Formulae for Extensions of Local Fields, and Conjectures on the Density of Number Field Discriminants