标题： 在黎曼曲面上行列式情况下的库仑气体的自由能 显示英文标题

标题： Free energy of the Coulomb gas in the determinantal case on Riemann surfaces

摘要： 我们推导了在任意亏格g的紧黎曼曲面上，库仑气体系统的分划函数的渐近展开式。 我们的主要工具是将分析扭结与几何量（包括该分划函数定义中出现的格林函数）联系起来的玻色化公式。 作为结果，我们在行列式情况下证明了扎布罗丁-维格曼猜想的几何版本。 显示英文摘要

摘要： We derive the asymptotic expansion of the partition function of a Coulomb gas system in the determinantal case on compact Riemann surfaces of any genus g. Our main tool is the bosonization formula relating the analytic torsion and geometric quantities including the Green functions appearing in the definition of this partition function. As a result, we prove the geometric version of the Zabrodin-Wiegmann conjecture in the determinantal case.