Tag Archives: MO

The class number 100 problem

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)

There’s a rumour going around that results from transcendence theory are required to prove the Fontaine-Mazur conjecture for . This is not correct. In Serre’s book on -adic representations, he defines a -adic representation of a global Galois group to … Continue reading

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Is this the worst MO question ever?

(Link here). To answer the question of the title, probably not. But it is a fantastic piece of nonsense, falling somewhere between Edward Lear and a reverse Sokal hoax.

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Jacobi by pure thought

JB asks whether there is a conceptual proof of Jacobi’s formula: Here (to me) the best proof is one that requires the least calculation, not necessarily the “easiest.” Here is my attempt. We use the following property of , which … Continue reading

Posted in Mathematics | Tagged , , | 4 Comments