On the p-adic geometry of traces of singular moduli

Details On the p-adic geometry of traces of singular moduli On the p-adic geometry of traces of singular moduli

2005-02-10

arxiv.org/abs/math/0502213v1

Int. J. Number Theory 1 (2005), no. 4, 495--497.

Mathematics

Number Theory

3 pages, Latex

Scientific paper

10.1142/S1793042105000327

The aim of this article is to show that p-adic geometry of modular curves is useful in the study of p-adic properties of traces of singular moduli. In order to do so, we partly answer a question by Ono. As our goal is just to illustrate how p-adic geometry can be used in this context, we focus on a relatively simple case, in the hope that others will try to obtain the strongest and most general results. For example, for p=2, a result stronger than Thm.1 is proved in [Boylan], and a result on some modular curves of genus zero can be found in [Osburn] . It should be easy to apply our method, because of its local nature, to modular curves of arbitrary level, as well as to Shimura curves.

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