Traces of CM values of modular functions

Details Traces of CM values of modular functions Traces of CM values of modular functions

2004-08-30

arxiv.org/abs/math/0408406v1

Mathematics

Number Theory

29 pages

Scientific paper

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 SL(2,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.

Affiliated with

Also associated with

No associations

Rating

Traces of CM values of modular functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Traces of CM values of modular functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Traces of CM values of modular functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-512527