By Jan H. Bruinier
Round 1994 R. Borcherds stumbled on a brand new kind of meromorphic modular shape at the orthogonal staff $O(2,n)$. those "Borcherds items" have endless product expansions analogous to the Dedekind eta-function. They come up as multiplicative liftings of elliptic modular varieties on $(SL)_2(R)$. the truth that the zeros and poles of Borcherds items are explicitly given when it comes to Heegner divisors makes them fascinating for geometric and mathematics purposes. within the current textual content the Borcherds' building is prolonged to Maass wave kinds and is used to review the Chern periods of Heegner divisors. A speak theorem for the lifting is proved.
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