COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Number Theory Seminar > Analytic continuation of Hilbert modular forms and applications to modularity

## Analytic continuation of Hilbert modular forms and applications to modularityAdd to your list(s) Download to your calendar using vCal - Payman Kassaei (King's College London)
- Tuesday 07 May 2013, 16:15-17:15
- MR13.
If you have a question about this talk, please contact Teruyoshi Yoshida. In his foundational work on the theory of p-adic modular forms, N. Katz observed that there is a positive lower bound for the “growth condition” of an overconvegent p-adic modular eigenform with nonzero Up-eigenvalue. In more modern language, this states that any such form can be analytically continued from its initial domain of definition to a not ”too small” region of the rigid analytic modular curve. Years later, K. Buzzard, by considering these forms in their true level (i.e., level divisible by p) proved that such forms can be further extended to a certain “large” region of the modular curve. These results were used by Buzzard and Taylor to prove modularity lifting results which led to a proof of certain cases of the Strong Artin conjecture. It has been known for a while how to extend these results to the Hilbert case when p is split in the totally real field of degree g > 1, as the problem looks formally like a product of g copies of the modular curve case. In the inert case, however, a mixing happens that fundamentally changes the nature of the problem. In this talk, I will explain new results on domains of automatic analytic continuation for overconvergent Hilbert modular forms in the case p is unramified in the totally real field. These results can be used to prove many cases of the strong Artin conjecture for Hilbert modular forms. Some of the work that will be presented is joint with Sasaki and Tian. This talk is part of the Number Theory Seminar series. ## This talk is included in these lists:- All CMS events
- All Talks (aka the CURE list)
- CMS Events
- DPMMS Lists
- DPMMS Pure Maths Seminar
- DPMMS info aggregator
- DPMMS lists
- MR13
- Number Theory Seminar
- School of Physical Sciences
Note that ex-directory lists are not shown. |
## Other listsProbability + Information Reading Group The Audrey Richards Annual Lecture in African Studies Institute of Astronomy Seminars## Other talksBuilding World Class Life Science Businesses – The Good, The Bad and The Ugly Metamaterials and the Science of Invisibility Glanville Lecture 2017/18: The Book of Exodus and the Invention of Religion Earth Observation Research Workshop A sex-linked supergene controls sperm morphology and swimming speed in a songbird Molecular wiring of a mitochondrial translation feedback loop |