Abelian Chern-Simons theory on the torus and physical views on the Hecke operators

Yasuhiro Abe

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arXiv · 1804.02848

Abelian Chern-Simons theory on the torus and physical views on the Hecke operators

Yasuhiro Abe

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Abstract

In the previous paper arXiv:1711.07122, we show that a holomorphic zero-mode wave function in abelian Chern-Simons theory on the torus can be considered as a quantum version of a modular form of weight 2. Motivated by this result, in this paper we consider an action of a Hecke operator on such a wave function from a gauge theoretic perspective. This leads us to obtain some physical views on the Hecke operators in number theory.

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Yasuhiro Abe. 2018-04-09. Abelian Chern-Simons theory on the torus and physical views on the Hecke operators. https://arxiv.org/abs/1804.02848

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