Explicit Gross-Zagier and Waldspurger Formulae
Li Cai, Jie Shu, and Ye Tian
TL;DR
This paper provides explicit formulas for the Gross-Zagier and Waldspurger relations on Shimura Curves, enhancing the understanding of their arithmetic properties and applications.
Contribution
It introduces explicit versions of the Gross-Zagier and Waldspurger formulas specifically for Shimura Curves, which were previously known in more abstract forms.
Findings
Explicit formulas derived for Gross-Zagier on Shimura Curves
Explicit Waldspurger formula established for specific cases
Enhanced tools for arithmetic applications of these formulas
Abstract
We give an explicit form of Gross-Zagier formula on Shimura Curves and an explicit form of Waldspurger formula.
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