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Traces of CM values of modular functions
-
Jan Hendrik Bruinier
and
Jens Funke
Published/Copyright:
May 17, 2006
Abstract
Zagier proved that the traces of singular moduli, i.e., the sums of the values of the classical j-invariant over quadratic irrationalities, are the Fourier coefficients of a modular form of weight 3/2 with poles at the cusps. Using the theta correspondence, we generalize this result to traces of CM values of (weakly holomorphic) modular functions on modular curves of arbitrary genus. We also study the theta lift for the weight 0 Eisenstein series for SL2(ℤ) and realize a certain generating series of arithmetic intersection numbers as the derivative of Zagier's Eisenstein series of weight 3/2. This recovers a result of Kudla, Rapoport and Yang.
Received: 2004-09-03
Published Online: 2006-05-17
Published in Print: 2006-05-01
© Walter de Gruyter
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- Représentations semi-stables de torsion dans le cas er < p − 1
- Zero cycles on a threefold with isolated singularities
- On the density of algebraic foliations without algebraic invariant sets
- Compactness of solutions to some geometric fourth-order equations
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Articles in the same Issue
- Traces of CM values of modular functions
- Représentations semi-stables de torsion dans le cas er < p − 1
- Zero cycles on a threefold with isolated singularities
- On the density of algebraic foliations without algebraic invariant sets
- Compactness of solutions to some geometric fourth-order equations
- Relative cohomology with respect to a Lefschetz pencil
- There are genus one curves of every index over every number field
- The uniqueness of Cuntz-Krieger type algebras
