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From the Ideal Theorem to the class number

Part of: Algebraic number theory: global fields

Published online by Cambridge University Press:  26 May 2023

Olivier Bordellès Open the ORCID record for Olivier Bordellès [Opens in a new window]
Olivier Bordellès*
Affiliation:
Lycée Dupuy, Le Puy-en-Velay, 2, allée de la Combe, Aiguilhe 43000, France
*
e-mail: [email protected]
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Abstract

In this article, we provide an explicit upper bound for $h_K \mathcal {R}_K d_K^{-1/2}$ which depends on an effective constant in the error term of the Ideal Theorem.

Keywords

Class numberDedekind zeta-functionIdeal Theorem

MSC classification

Primary: 11R29: Class numbers, class groups, discriminants 11R42: Zeta functions and $L$-functions of number fields
Type
Article
Information
Canadian Mathematical Bulletin , Volume 66 , Issue 4 , December 2023 , pp. 1368 - 1375
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Canadian Mathematical Society

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