Algebra & Number Theory

Explicit Gross–Zagier and Waldspurger formulae

Li Cai, Jie Shu, and Ye Tian

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We give an explicit Gross–Zagier formula which relates the height of an explicitly constructed Heegner point to the derivative central value of a Rankin L-series. An explicit form of the Waldspurger formula is also given.

Article information

Algebra Number Theory, Volume 8, Number 10 (2014), 2523-2572.

Received: 3 October 2014
Revised: 21 October 2014
Accepted: 23 November 2014
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11G40: $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture [See also 14G10]

Gross–Zagier formula Waldspurger formula Heegner points periods


Cai, Li; Shu, Jie; Tian, Ye. Explicit Gross–Zagier and Waldspurger formulae. Algebra Number Theory 8 (2014), no. 10, 2523--2572. doi:10.2140/ant.2014.8.2523.

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