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Наука и учебаBorcherds Products on O(2,l) and Chern Classes of Heegner Divisors (Lecture Notes in Mathematics)

Borcherds Products on O(2,l) and Chern Classes of Heegner Divisors (Lecture Notes in Mathematics)
Название:Borcherds Products on O(2,l) and Chern Classes of Heegner Divisors (Lecture Notes in Mathematics)
Автор:Jan H. Bruinier
Издательство:Springer
ISBN:3540433201
Дата издания:2002-05-31
Страниц:160
Язык:Английский
Формат:PDF
Размер: 1.28 MB

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.





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