Partial classicality of Hilbert modular forms
Chi-Yun Hsu (UCLA)
Abstract: Overconvergent Hilbert modular forms are defined over a strict neighborhood of the ordinary locus of the Hilbert modular variety. The philosophy of classicality theorems is that when the valuation of $U_p$-eigenvalues are small enough (called a small slope condition), an overconvergent Hecke eigenform is automatically classical, namely, it can be defined over the whole Hilbert modular variety. On the other hand, we can define partially classical forms as forms defined over a strict neighborhood of a “partially ordinary locus”. We show that under a weaker small slope condition, an overconvergent form is automatically partially classical. We adapt Kassaei’s method of analytic continuation.
number theory
Audience: researchers in the topic
Dublin Algebra and Number Theory Seminar
Series comments: Passcode: The 3-digit prime numerator of Riemann zeta at -11
Organizers: | Kazim Buyukboduk*, Robert Osburn |
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