English

Traces of singular values and Borcherds products

Number Theory 2007-05-23 v2

Abstract

Let pp be a prime for which the congruence group Γ0(p)\Gamma_0(p)^* is of genus zero, and jpj_p^* be the corresponding Hauptmodul. Let ff be a nearly holomorphic modular form of weight 1/2 on Γ0(4p)\Gamma_0(4p) which satisfies some congruence condition on its Fourier coefficients. We interpret ff as a vector valued modular form. Applying Borcherds lifting of vector valued modular forms we construct infinite products associated to jpj_p^* and extend Zagier's trace formula for singular values of jpj_p^*. Further we investigate the twisted traces of sigular values of jpj_p^* and construct Borcherds products related to them.

Keywords

Cite

@article{arxiv.math/0305183,
  title  = {Traces of singular values and Borcherds products},
  author = {Chang Heon Kim},
  journal= {arXiv preprint arXiv:math/0305183},
  year   = {2007}
}

Comments

21 pages

R2 v1 2026-07-22T16:54:31.698Z