Tag Archives: Hilbert modular forms

SL_n versus GL_n

Posted on July 18, 2024 by Persiflage

I recently wrote a paper (with Toby Gee and George Boxer, see also here) on constructing regular algebraic automorphic representations \(\pi\) of (cohomological) weight zero and level one, and therefore also cuspidal cohomology classes in the cohomology of \(\mathrm{GL}_n(\mathbf{Z})\) for … Continue reading →

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More on Lehmer’s Conjecture

Posted on March 21, 2020 by Persiflage

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 →

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Dembélé on Abelian Surfaces with good reduction everywhere

Posted on March 27, 2019 by Persiflage

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 →

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En Passant IV

Posted on July 19, 2014 by Persiflage

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 →

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Hilbert Modular Forms of Partial Weight One, Part II

Posted on December 8, 2012 by Persiflage

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 →

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Hilbert Modular Forms of Partial Weight One, Part I

Posted on October 13, 2012 by Persiflage

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 →

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