On the $p$-adic periods of the modular curve $X(\Gamma _0(p) \cap \Gamma (2))$
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- by Adel Betina and Emmanuel Lecouturier PDF
- Trans. Amer. Math. Soc. 371 (2019), 413-429 Request permission
Abstract:
We prove a variant of Oesterlé’s conjecture describing $p$-adic periods of the modular curve $X_0(p)$, with an additional $\Gamma (2)$-structure (and also $\Gamma (3) \cap \Gamma _0(p)$ if $p \equiv 1 \bmod {3}$). We use de Shalit’s techniques and $p$-adic uniformization of curves with semi-stable reduction.References
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Additional Information
- Adel Betina
- Affiliation: Facultat de Matemàtiques i Estadística, Universitat Politècnica de Catalunya, C. Jordi Girona, 31.08034 Barcelona, Spain
- Address at time of publication: School of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, United Kingdom
- Email: A.Betina@shef.ac.uk
- Emmanuel Lecouturier
- Affiliation: Département des Mathématiques, Université Paris 7, 5 Rue Thomas Mann, 75013, Paris, France
- MR Author ID: 969451
- Email: emmanuel.lecouturier@imj-prg.fr
- Received by editor(s): November 24, 2016
- Received by editor(s) in revised form: March 3, 2017
- Published electronically: May 30, 2018
- Additional Notes: The first author has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 682152). The second author has received funding from the Université Paris $7$ for his PhD thesis.
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 413-429
- MSC (2010): Primary 11580
- DOI: https://doi.org/10.1090/tran/7236
- MathSciNet review: 3885149