Year: 2022
Type: preprint
Abstract: The goal of this paper is to prove a formula expressing the modular height of a quaternionic Shimura curve over a totally real number field in terms of the logarithmic derivative of the Dedekind zeta function of the totally real number field. Our proof is based on the work of Yuan-Zhang-Zhang on the Gross-Zagier formula and the work of Yuan-Zhang on the averaged Colmez conjecture. All these works are in turn inspired by the Pioneering work of Gross-Zagier and some philosophies of Kudla's program.
Source: arXiv (Cornell University)
Author: Yuan, Xinyi
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4320458565