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A mod-$p$ Artin–Tate
conjecture, and generalizing the Herbrand–Ribet theorem
Dipendra Prasad |
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Vol. 303 (2019), No. 1, 299–316
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DOI: 10.2140/pjm.2019.303.299
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Abstract |
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We propose conjectures about the integrality properties of the values at of certain abelian -functions of and totally real number fields. We also propose a conjecture which generalizes the theorems of Herbrand and Ribet for values at of totally odd Artin -functions of totally real number fields. Various calculations, some of which are familiar to experts, are made to provide examples. |
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Keywords
class groups, class number formula, Iwasawa theory, main
conjecture, $L$-values, algebraicity of $L$-values,
Herbrand–Ribet theorem
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Mathematical Subject Classification 2010
Primary: 11F33, 11R23
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Milestones
Received: 10 March 2018
Revised: 5 April 2019
Accepted: 6 April 2019
Published: 21 December 2019
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Authors |
| Dipendra Prasad | ||
| Indian Institute of Technology
Bombay Mumbai India |
School of Mathematics Tata Institute of Fundamental Research Mumbai India |
Laboratory of Modern Algebra and
Applications Saint Petersburg State University Saint Petersburg Russia |
