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  • Borcherds Products on 0(2,1) and Chern Classes of Heegner Divisors

    By Jan Hendrik Bruinier

    Our Price: $49.95
    • Format: Paperback
    • ISBN-13: 9783540433200
    • Publisher: Springer Verlag
    • Published: September 2002
    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.
  • The 1-2-3 of Modular Forms

    By Jan Hendrik Bruinier

    Our Price: $74.99
    • Format: Paperback
    • ISBN-13: 9783540741176
    • Publisher: Springer Verlag
    • Published: May 2008
    This book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture.Each part treats a number of beautiful applications.

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