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On the root of unity ambiguity in a formula for the Brumer–Stark units

Part of: Algebraic number theory: global fields

Published online by Cambridge University Press:  27 December 2023

Matthew H. Honnor Open the ORCID record for Matthew H. Honnor [Opens in a new window]
Matthew H. Honnor*
Affiliation:
Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
*
e-mail: m.honnor@imperial.ac.uk
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Abstract

We prove a conjectural formula for the Brumer–Stark units. Dasgupta and Kakde have shown the formula is correct up to a bounded root of unity. In this paper, we resolve the ambiguity in their result. We also remove an assumption from Dasgupta–Kakde’s result on the formula.

Keywords

Brumer–Stark unitsL-functionsTotally real fields

MSC classification

Primary: 11R80: Totally real fields 11R27: Units and factorization 11R42: Zeta functions and $L$-functions of number fields

Information

Type
Article
Information
Canadian Mathematical Bulletin , Volume 67 , Issue 3 , September 2024 , pp. 611 - 623
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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