The University of Arizona

Upper bounds for constant slope p-adic families of modular forms

Upper bounds for constant slope p-adic families of modular forms

Series: Algebra and Number Theory Seminar
Location: ENR2 S395
Presenter: John Bergdall, Bryn Mawr

This talk is concerned with the radius of convergence of p-adic families of modular forms --- q-series over a p-adic disc whose specialization to certain integer points is the q-expansion of a classical Hecke eigenform of level p. Numerical experiments by Gouvêa and Mazur in the nineties predicted the general existence of such families but also suggested, in spirit, the radius of convergence in terms of an initial member. Buzzard and Calegari showed, ten years later, that the Gouvêa--Mazur prediction was false. It has since remained open question how to salvage it. Here we will present some recent theoretical results towards such a salvage, backed up by numerical data.

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