An application of the \(p\)-adic class number formula

DOI10.1007/BF02677487zbMath0886.11061MaRDI QIDQ1365307

Tauno Metsänkylä

Publication date: 28 January 1998

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/156315

zbMATH Keywords

class number\(p\)-adic \(L\)-function\(p\)-divisibilityreal abelian field

Mathematics Subject Classification ID

Class numbers, class groups, discriminants (11R29) Zeta functions and (L)-functions of number fields (11R42) Cyclotomic extensions (11R18) Zeta functions and (L)-functions (11S40) Class field theory; (p)-adic formal groups (11S31) Other abelian and metabelian extensions (11R20)

Related Items

Triviality of Iwasawa module associated to some abelian fields of prime conductors ⋮ Unnamed Item ⋮ Indivisibility of the class number of a real abelian field of prime conductor ⋮ On divisibility of the class number \(h^+\) of the real cyclotomic fields \(\mathbb{Q}(\zeta_p+\zeta_p^{-1})\) by primes \(q\leq 5000\) ⋮ Unnamed Item ⋮ Note on the Class Number of the pth Cyclotomic Field, II ⋮ Relative class numbers inside the \(p\)th cyclotomic field ⋮ A condition for divisibility of the class number of real \(p\)th cyclotomic field by an odd prime distinct from \(p\) ⋮ Class number of real abelian fields ⋮ Note on the class number of the \(p\)th cyclotomic field ⋮ On the class number of a real abelian field of prime conductor ⋮ On the computation of class numbers of real abelian fields ⋮ Note on Bernoulli numbers associated to some Dirichlet character of prime conductor

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Über Klassenzahlprimteiler reeller abelscher Zahlkörper als Primteiler verallgemeinerter Bernoullischer Zahlen
• Über Fermatquotienten von Kreiseinheiten und Klassenzahlformen modulo \(p\)
• On divisibility of class number of real abelian fields of prime conductor
• Connection between congruences \(n^{q-1}\equiv 1 \pmod {q^ 2}\) and divisibility of \(h^ +\)
• On divisibility of the class number \(h^+\) of the real cyclotomic fields \(\mathbb{Q}(\zeta_p+\zeta_p^{-1})\) by primes \(q\leq 5000\)
• On the divisibility of \(h^+\) by the prime 3
• Generalized Dedekind sums and transformation formulae of certain Lambert series
• Eine p-adische Theorie der Zetawerte. II.
• On divisibility of the class number ℎ⁺ of the real cyclotomic fields of prime degree 𝑙
• Connection between the Wieferich congruence and divisibility of h⁺
• Zur Arithmetik in abelschen Zahlkörpern.