Differential modular forms over totally real fields of integral weights

Banerjee, Debargha; Saha, Arnab

doi:10.1007/s40993-021-00269-7

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Differential modular forms over totally real fields of integral weights

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Saha, Arnab
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s40993-021-00269-7
(Publisher version)

https://doi.org/10.48550/arXiv.1806.00191
(Preprint)

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Citation

Banerjee, D., & Saha, A. (2021). Differential modular forms over totally real fields of integral weights. Research in Number Theory, 7(3): 42. doi:10.1007/s40993-021-00269-7.

Cite as: https://hdl.handle.net/21.11116/0000-0008-C388-2

Abstract

In this article, we construct a differential modular form of non-zero order and integral weight for compact Shimura curves over totally real fields bigger than Q. The construction uses the theory of lifting ordinary mod p Hilbert modular forms to characteristic 0 as well as the theory of Igusa curve. This is the analogue of the construction of Buium in the case of modular curves parametrizing elliptic curves with level structures.