Abstract
This article studies the first-order p-adic deformations of classical weight one newforms, relating their fourier coefficients to the p-adic logarithms of algebraic numbers in the field cut out by the associated projective Galois representation.
This is a preview of subscription content, log in via an institution to check access.
References
Bellaïche, J., Dimitrov, M.: On the eigencurve at classical weight one points. Duke Math. J. 165(2), 245–266 (2016)
Buzzard, K., Lauder, A.: A computation of modular forms of weight one and small level. Ann. Math. Québec. 41(2), 213–219 (2017). Appendix http://people.maths.ox.ac.uk/lauder/weight1
Darmon, H., Lauder, A., Rotger, V.: Overconvergent generalised eigenforms of weight one and class fields of real quadratic fields. Adv. Math. 283, 130–142 (2015)
Darmon, H., Lauder, A., Rotger, V.: Stark points and p-adic iterated integrals attached to modular forms of weight one. Forum Math. Pi 3, e8, 95 (2015)
Darmon, H., Lauder, A., Rotger, V.: Elliptic Stark conjectures and irregular weight one forms (in progress)
Duke, W., Li, Y.: Harmonic Maass forms of weight 1. Duke Math. J. 164(1), 39–113 (2015)
Lauder, A.: Computations with classical and p-adic modular forms. LMS J. Comput. Math. 14, 214–231 (2011)
Mazur, B.: Deforming Galois representations. In: Galois Groups Over \(\mathbb {Q}\) (Berkeley, CA, 1987). Mathematical Sciences Research Institute Publication, vol. 16, pp. 395–437. Springer, New York (1989)
Acknowledgements
The first author was supported by an NSERC Discovery grant, and the third author was supported by Grant MTM2015-63829-P. The second author would like that thank Takeshi Saito of Tokyo University and Kenichi Bannai of Keio University for their hospitality. This project 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 third author also acknowledges financial support from the Spanish Ministry of Economy and Competitiveness, through the María de Maeztu Programme for Units of Excellence in R&D (MDM-2014-0445).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Darmon, H., Lauder, A., Rotger, V. (2017). First Order p-Adic Deformations of Weight One Newforms. In: Bruinier, J., Kohnen, W. (eds) L-Functions and Automorphic Forms. Contributions in Mathematical and Computational Sciences, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-319-69712-3_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-69712-3_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-69711-6
Online ISBN: 978-3-319-69712-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)