Difference of a Hauptmodul for $\Gamma_{0}(N)$ and certain Gross-Zagier type CM value formulas

Dongxi Ye

Difference of a Hauptmodul for $\Gamma_{0}(N)$ and certain Gross-Zagier type CM value formulas

Number Theory 2021-01-12 v2

Authors: Dongxi Ye

Abstract

In this work, we show that the difference of a Hauptmodul for a genus zero group $\Gamma_{0}(N)$ as a Hilbert modular function on $Y_{0}(N)\times Y_{0}(N)$ is a Borcherds lift of type $(2,2)$ . As applications, we derive Monster denominator formula like product expansions for these Hilbert modular functions and certain Gross-Zagier type CM value formulas.

Keywords

Hauptmodul Gamma_0(N) Hilbert modular function Borcherds lift Gross-Zagier type CM value formula genus zero group

Cite

@article{arxiv.1708.08783,
  title  = {Difference of a Hauptmodul for $\Gamma_{0}(N)$ and certain Gross-Zagier type CM value formulas},
  author = {Dongxi Ye},
  journal= {arXiv preprint arXiv:1708.08783},
  year   = {2021}
}

Comments

Accepted for publication in SCIENCE CHINA Mathematics. arXiv admin note: text overlap with arXiv:1701.08433

Difference of a Hauptmodul for $\Gamma_{0}(N)$ and certain Gross-Zagier type CM value formulas

Abstract

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