Algebra & Number Theory

Explicit Gross–Zagier and Waldspurger formulae

Li Cai, Jie Shu, and Ye Tian

Full-text: Open access

Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ant/1513730332

Digital Object Identifier
doi:10.2140/ant.2014.8.2523

Mathematical Reviews number (MathSciNet)
MR3298547

Zentralblatt MATH identifier
1311.11054

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

Keywords
Gross–Zagier formula Waldspurger formula Heegner points periods

Citation

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. https://projecteuclid.org/euclid.ant/1513730332


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