Borcherds Products on O(2,l) and Chern Classes of Heegner Divisors
Jan H. Bruinier
Around 1994 R. Borcherds discovered a new type of meromorphic modular form on the orthogonal group $O(2,n)$. These "Borcherds products" have infinite product expansions analogous to the Dedekind eta-function. They arise as multiplicative liftings of elliptic modular forms on $(SL)_2(R)$. The fact that the zeros and poles of Borcherds products are explicitly given in terms of Heegner divisors makes them interesting for geometric and arithmetic applications. In the present text the Borcherds' construction is extended to Maass wave forms and is used to study the Chern classes of Heegner divisors. A converse theorem for the lifting is proved.
Categories:
Year:
2002
Edition:
1
Publisher:
Springer
Language:
english
Pages:
168
ISBN 10:
3540433201
ISBN 13:
9783540433200
Series:
Lecture Notes in Mathematics
File:
PDF, 751 KB
IPFS:
,
english, 2002
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