Triple symbols in arithmetic
Dohyeong Kim, Masanori Morishita

TL;DR
This paper introduces a cohomological formulation of a mod n triple symbol in arithmetic, inspired by Chern–Simons theory, and demonstrates its consistency with existing definitions for specific cases.
Contribution
It presents a novel cohomological approach to defining mod n triple symbols in arithmetic, extending previous work and connecting to topological concepts.
Findings
The new symbol aligns with Rédéi's for n=2.
It agrees with Amano–Mizusawa–Morishita's for n=3.
Provides a unified cohomological framework for triple symbols.
Abstract
Triple symbols are arithmetic analogues of the mod triple linking number in topology, where is an integer. In this paper, we introduce a cohomological formulation of a mod triple symbol for characters over a number field containing a primitive -th root of unity. Our definition is motivated by the arithmetic Chern--Simons theory and in this respect it differs from earlier approaches to triple symbols. We show that our symbol agrees with that of R\'edei when and of Amano--Mizusawa--Morishita when .
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Advanced Algebra and Logic · Mathematics and Applications
