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ABC Conjecture

For the 1998 Arizona Winter School, a group of students at The University of Arizona studied a paper by Dorian Goldfeld and Lucien Szpiro, which claims to asymptotically bound the order of the Tate--Shafarevich group by N1/2+ε. In our talk, we showed the correct bound to be N3/4+ε. Some material from our talk is available:

Slides (version: March 1999) from our March 1998 talk:

Some GP/PARI code for computing the Szpiro number:

Related work: