标题： 希尔伯特欧拉级数作为土井–长糠升 lifts 显示英文标题

标题： Hilbert Eisenstein series as Doi-Naganuma lift

摘要： 本文中，我们证明了实二次域上的非相干Hilbert Eisenstein级数可以表示为一个非相干Eisenstein级数的Doi-Naganum提升，该级数定义于$\mathbb{Q}$上。作为应用，我们证明当$N$是奇数且无平方因子时，若判别式足够大，则在$X_0(N)^2$上Borcherds乘积在有效除子上的Heegner点值不是积分单位。这将第一作者的结果推广到了更高水平的情形。在此过程中，我们明确描述了当二次空间具有(2, 2)型签名时，Bruinier-Kudla-Yang工作中出现的Rankin-Selberg型L函数，并给出了出现在有限二次模Weil表示中的基本不变向量的一个新构造。 显示英文摘要

摘要： In this paper, we show that incoherent Hilbert Eisenstein series for a real quadratic fields can be expressed as the Doi-Naganums lift of an incoherent Eisenstein series over $\mathbb{Q}$. As an application, we show when $N$ is odd and square-free, the values at Heegner points of Borcherds product on $X_0(N)^2$ with effective divisors are not integral units when the discriminants are sufficiently large. This generalizes a result of the first author to higher levels. In the process, we explicitly describe the Rankin-Selberg type L-function that appeared in the work of Bruinier-Kudla-Yang when the quadratic space has signature (2, 2), and give a new construction of fundamental invariant vectors appearing in Weil representations of finite quadratic modules.