论文标题
Adelic措施的内部产品：应用于Arakelov-Zhang配对
An Inner Product on Adelic Measures: With Applications to the Arakelov-Zhang Pairing
论文作者
论文摘要
我们在一个数字字段上的Adelic度量的矢量空间上定义了内部产品。我们发现，这种内部产品引起的规范控制着$ k $的每个地方的弱收敛性。与有理图相关的规范adelic度量是在此矢量空间中，而两种此类adelic测量值差的正方形是来自算术动力学的Arakelov-Zhang配对。我们证明，在阿德莱克度量的标准上，尖锐的下限具有小的adelic高度。我们发现，与有理图相关的规范adelic度量的规范与Arakelov的高度相称。结果，两个合理地图$ f $和$ g $的Arakelov-Zhang配对可以从下面界定为$ g $。
We define an inner product on a vector space of adelic measures over a number field. We find that the norm induced by this inner product governs weak convergence at each place of $K$. The canonical adelic measure associated to a rational map is in this vector space, and the square of the norm of the difference of two such adelic measures is the Arakelov-Zhang pairing from arithmetic dynamics. We prove a sharp lower bound on the norm of adelic measures with points of small adelic height. We find that the norm of a canonical adelic measure associated to a rational map is commensurate with the Arakelov height on the space of rational functions with fixed degree. As a consequence, the Arakelov-Zhang pairing of two rational maps $f$ and $g$ can be bounded from below as a function of $g$.
