General information
- Members of the research group
- The number theory mailing list
- Link to the Cryptography research group
Research
- Preprints by members of the research group
- Algebraic and Analytic Methods in Number Theory (EPSRC grant no. EP/F060661/1)
- Rational Points on Algebraic Varieties (EPSRC grant no. GR/R93155/01)
- Papers by members of the group, on the departmental eprint server
Seminars
- Number theory seminars
- Next seminar: 22 November 201816:00Alice PozziAbstract
In 1973, Serre observed that the Hecke eigenvalues of Eisenstein series can be p-adically interpolated. In other words, Eisenstein series can be viewed as specializations of a p-adic family parametrized by the weight. The notion of p-adic variations of modular forms was later generalized by Hida to include families of ordinary cuspforms. In 1998, Coleman and Mazur defined the eigencurve, a rigid analytic space classifying much more general p-adic families of Hecke eigenforms parametrized by the weight. The local nature of the eigencurve is well-understood at points corresponding to cuspforms of weight k ≥ 2, while the weight one case is far more intricate.
In this talk, we discuss the geometry of the eigencurve at weight one Eisenstein points. Our approach consists in studying the deformation rings of certain (deceptively simple!) Artin representations. Via this Galois-theoretic method, we obtain the q-expansion of some non-classical overconvergent forms in terms of p-adic logarithms of p-units in certain number field. Finally, we will explain how these calculations suggest a different approach to the Gross-Stark conjecture.
- Next seminar:
- Junior number theory seminars
- Next seminar: There are no seminars currently scheduled for this series.
- Next seminar:
Other information
- Information for Applicants for Postgraduate study
- Travel information
- Vacancies within the department