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Borcherds products in the arithmetic intersection theory of Hilbert modular surfaces
, 2004
"... We prove an arithmetic version of a theorem of Hirzebruch and Zagier saying that HirzebruchZagier divisors on a Hilbert modular surface are the coefficients of an elliptic modular form of weight two. Moreover, we determine the arithmetic selfintersection number of the line bundle of modular forms e ..."
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We prove an arithmetic version of a theorem of Hirzebruch and Zagier saying that HirzebruchZagier divisors on a Hilbert modular surface are the coefficients of an elliptic modular form of weight two. Moreover, we determine the arithmetic selfintersection number of the line bundle of modular forms equipped with its Petersson metric on a regular model of a Hilbert modular surface, and study Faltings heights of
Infinite products in number theory and geometry
"... Abstract. We give an introduction to the theory of Borcherds products and to some number theoretic and geometric applications. In particular, we discuss how the theory can be used to study the geometry of Hilbert modular surfaces. 1. ..."
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Abstract. We give an introduction to the theory of Borcherds products and to some number theoretic and geometric applications. In particular, we discuss how the theory can be used to study the geometry of Hilbert modular surfaces. 1.
16. THE CONNECTION TO EISENSTEIN SERIES by
"... In a previous chapter [Go2] an expression was obtained for the arithmetic intersection number of three modular correspondences (Tm1 · Tm2 · Tm3), when their intersection is of dimension 0. This expression is quite complicated, and involves certain local representation densities β`(Q) of quadratic ..."
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In a previous chapter [Go2] an expression was obtained for the arithmetic intersection number of three modular correspondences (Tm1 · Tm2 · Tm3), when their intersection is of dimension 0. This expression is quite complicated, and involves certain local representation densities β`(Q) of quadratic forms and a local intersection
RESEARCH STATEMENT MODULAR FORMS AND CYCLES IN LOCALLY SYMMETRIC SPACES AND SHIMURA VARIETIES: INTERPLAY BETWEEN AUTOMORPHIC FORMS, REPRESENTATION THEORY, AND ARITHMETIC AND DIFFERENTIAL GEOMETRY
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