Norms of Singular Moduli

Norms of Singular Moduli

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Shilin Lai, Princeton University
Fine Hall 110

The j-function is a special modular function on the upper half plane. Its values at imaginary quadratic points are called singular moduli. It is a classical result that they are always algebraic integers. In 1983, Zagier discovered an explicit formula for the prime factorizations of their norms. This talk will sketch his analytical proof of this result, after recalling the necessary background material.