A proof of the refined class number formula of Gross
Minoru Hirose
TL;DR
This paper proves Gross's conjectural congruence linking Stickelberger elements and algebraic regulators, confirming a significant aspect of the refined class number formula proposed in 1988.
Contribution
The paper provides a proof of Gross's conjecture, establishing the refined class number formula's validity.
Findings
Proof of Gross's conjectural congruence
Validation of the refined class number formula
Advancement in algebraic number theory
Abstract
In 1988, Gross proposed a conjectural congruence between Stickelberger elements and algebraic regulators, which is often referred to as the refined class number formula. In this paper, we prove this congruence.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Advanced Algebra and Geometry