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Meta
Tag Archives: Hilbert modular forms
More on Lehmer’s Conjecture
Lehmer said it was a “natural question” whether there existed an integer such that \(\tau(n)=0\) or not. I’ve wondered a little bit recently about how reasonable this is. (See this post.) The historical context is presumably related to the fact … Continue reading
Dembélé on Abelian Surfaces with good reduction everywhere
New paper by Dembélé (friend of the blog) on abelian surfaces with good reduction everywhere (or rather, the lack of them for many real quadratic fields of small discriminant). I have nothing profound to say about the question of which … Continue reading
En Passant IV
My students Richard Moy and Joel Specter have uploaded their paper on partial weight one Hilbert modular forms, previously discussed here, to the ArXiv. Germany now leads the world in both soccer and perfectoid spaces. This is a recipe for … Continue reading
Posted in Waffle
Tagged Bourgeois Pig, Carbon Tax, Cortado, Dinosaur Comics, Existential Comics, Gibraltar, Grue, Hilbert modular forms, Intelligentsia, Joel Specter, Justice, Little Johnny Howard, Matthew Emerton, Perfectoid Spaces, Richard Moy, SiriusXM, Soccer, Toby Gee, Tony Abbott
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Hilbert Modular Forms of Partial Weight One, Part II
Anyone who spends any time thinking about Hilbert modular forms of partial weight one — see part I — should, at some point, wonder whether there actually exist any examples, besides the “trivial” examples arising as inductions of Grossencharacters. Fred … Continue reading
Posted in Mathematics, Students
Tagged Existence, Fred Diamond, Hilbert modular forms, Joel Specter, Richard Moy
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Hilbert Modular Forms of Partial Weight One, Part I
Let \(\pi\) be an algebraic Hilbert modular cuspform for some totally real field \(F^{+}\). Then, associated to \(\pi\), one has a compatible family of Galois representations: \(r_{\lambda}(\pi): G_{F^{+}} \rightarrow \mathrm{GL}_2(\mathcal{O}_{\lambda})\) which are unramified outside finitely many primes (this is the … Continue reading