Tag Archives: MO

The class number 100 problem

Posted on January 19, 2017 by Persiflage

Some time ago, Mark Watkins busted open the “class number n” problem for smallish n, finding all imaginary quadratic fields of class number at most 100 (the original paper is here) Although the paper describes the method in detail, it … Continue reading →

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A public service announcement concerning Fontaine-Mazur for GL(1)

Posted on July 12, 2014 by Persiflage

There’s a rumour going around that results from transcendence theory are required to prove the Fontaine-Mazur conjecture for \(\mathrm{GL}(1)\). This is not correct. In Serre’s book on \(\ell\)-adic representations, he defines a \(p\)-adic representation \(V\) of a global Galois group … Continue reading →

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Jacobi by pure thought

Posted on October 26, 2012 by Persiflage

JB asks whether there is a conceptual proof of Jacobi’s formula: \(\Delta = q \prod_{n=1}^{\infty}(1 – q^n)^{24}\) Here (to me) the best proof is one that requires the least calculation, not necessarily the “easiest.” Here is my attempt. We use … Continue reading →

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