2025/06/02 by Yingkun Li, Mingkuan Zhang, Li, Yingkun +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry
paper · pdf · doi:10.48550/arxiv.2506.01688
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 ℚ. As an application, we show when N is odd and square-free, the values at Heegner points of Borcherds product on X0(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.