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arXiv · 2008.11461

Magnetized Riemann Surface of Higher Genus and Eta Quotients of Semiprime Level

Masaki Honda
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Abstract

We study the zero mode solutions of a Dirac operator on a magnetized Riemann surface of higher genus. In this paper, we define a Riemann surface of higher genus as a quotient manifold of the Poincar$\acute{\text{e}}$ upper half-plane by a congruence subgroup, especially $Γ_{0}(N)$. We present a method to construct basis of cusp forms since the zero mode solutions should be cusp forms. To confirm our method, we select a congruence subgroup of semiprime level and show the demonstration to some lower weights. In addition, we discuss Yukawa couplings and matrix regularization as applications.

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Masaki Honda. 2020-08-26. Magnetized Riemann Surface of Higher Genus and Eta Quotients of Semiprime Level. https://arxiv.org/abs/2008.11461

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