Abstract
In this note, we will apply the results of Gross–Zagier, Gross–Kohnen–Zagier and their generalizations to give a short proof that the differences of singular moduli are not units. As a consequence, we obtain a result on isogenies between reductions of CM elliptic curves.
Subject
Algebra and Number Theory
Reference21 articles.
1. Heegner points and derivatives ofL-series. II
2. Eisenstein series for SL(2)
3. BEY19 Bruinier, J. H. , Ehlen, S. and Yang, T. , CM values of higher automorphic Green functions for orthogonal groups, Invent. Math., to appear. Preprint (2019), arXiv:1912.12084.
4. CM Number Fields and Modular Forms
5. Borcherds Products on O(2, l) and Chern Classes of Heegner Divisors
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