Potential role of the elliptic modular j-function in the "Kronecker's dream of youth" for real quadratic fields

虽然我们还没有成功地从椭圆模j-函数的“值”中得到任何算术量，但我们已经得到了关于Markoff数的一些算术结果。利用Markoff数的Farey参数化，给出了j-函数值在Markoff无理数处的一种丢番图连续性.

Although we have not yet succeeded in obtaining any arithmetic quantities from the "values" of the elliptic modular j-function, we have obtained on the way some arithmetic results concerning Markoff numbers. We have formulated a kind of Diophantine continuity of the values of j-function at Markoff irrationalities in terms of Farey parametrization of Markoff numbers.