Tag Archives: Sato-Tate

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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Update on Sato-Tate for abelian surfaces

Posted on July 19, 2018 by Persiflage

Various people have asked me for an update on the status of the Sato-Tate conjecture for abelian surfaces in light of recent advances in modularity lifting theorems. My student Noah Taylor has exactly been undertaking this task, and this post … Continue reading →

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The boundaries of Sato-Tate, part I

Posted on April 8, 2018 by Persiflage

A caveat: the following questions are so obvious that they have surely been asked elsewhere, and possibly given much more convincing answers. References welcome! The Sato-Tate conjecture implies that the normalized trace of Frobenius \(b_p \in [-2,2]\) for a non-CM … Continue reading →

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Complain about MSRI day

Posted on February 28, 2017 by Persiflage

I will be heading off later this week to the Academic Sponsors’ Day at MSRI, going as Shmuel’s proxy for uchicago. I’m not sure to what extent (if any) there is for me to make policy suggestions, but any comments … Continue reading →

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