Faltings heights of CM cycles and derivatives of L-functions

By Jan H. Bruinier, Tonghai Yang. 2008

105 citations recorded by the source corpus.

We study the Faltings height pairing of arithmetic special divisors and CM cycles on Shimura varieties associated to orthogonal groups. We compute the Archimedean contribution to the height pairing and derive a conjecture relating the total pairing to the central derivative of a Rankin L-function. We prove the conjecture in certain cases where the Shimura variety has dimension 0, 1, or 2. In particular, we obtain a new proof of the Gross-Zagier formula.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9542e67135ae34df5be2ae1d946fb7ee92fc50d0

How researchers see this paper

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In Algebra and Number Theory

1. Ken Ichi Ono
2. Kathrin Bringmann
3. Jeremy Lovejoy
4. Heng Huat Chan
5. Stephanie Treneer
6. Zhi-Wei Sun
7. Dermot McCarthy
8. Robert C. Rhoades

In Geometry and Topology

1. Ken Ichi Ono
2. Dermot McCarthy
3. Kathrin Bringmann
4. T. Kilbourn

In Mathematical Physics

1. Ken Ichi Ono
2. Kathrin Bringmann

Citations in the corpus

• Unearthing the visions of a master: harmonic Maass forms and number theory (2008, background): “In addition to formulating a deep conjecture about derivatives of L-functions and heights (see Section 15.2), they have proved the following striking theorem (see [70]).”