COLLOQUIO DE GIORGI

Dorian Goldfeld Columbia University

"On Gauss' class number problem"

Abstract

Gauss conjectured that his tables of class numbers published in the Disquisitiones Arithmeticae in 1801 were complete and that there should be an effective algorithm to determine all imaginary quadratic fields with a given class number. While visiting Pisa, 1974-1975, I showed that Gauss' conjecture could be reduced to a special case of the Birch-Swinnerton-Dyer conjecture on elliptic curves. This conjecture was solved by Gross-Zagier in 1984 and then the three of us won the Cole Prize in number theory shortly after that for the solution of Gauss' conjecture on class numbers. This talk will outline the history of the problem and some ideas of the solution.

Martedì 8 novembre 2005 ore 17.00

Aula Mancini

Palazzo della Carovana

Piazza dei Cavalieri, 7

PISA

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