Vol. 8, No. 10, 2014

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Explicit Gross–Zagier and Waldspurger formulae

Li Cai, Jie Shu and Ye Tian

Vol. 8 (2014), No. 10, 2523–2572
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.

Keywords
Gross–Zagier formula, Waldspurger formula, Heegner points, periods
Mathematical Subject Classification 2010
Primary: 11G40
Milestones
Received: 3 October 2014
Revised: 21 October 2014
Accepted: 23 November 2014
Published: 31 December 2014
Authors
Li Cai
Mathematical Sciences Center
Tsinghua University
Jin Chun Yuan West Bldg. 248
Beijing, 100084
China
Jie Shu
Academy of Mathematics and Systems Science
Morningside Center of Mathematics
Chinese Academy of Sciences
Beijing, 100190
China
Ye Tian
Academy of Mathematics and Systems Science
Morningside Center of Mathematics
Chinese Academy of Sciences
Beijing, 100190
China