Deformations of Theta Integrals and A Conjecture of Gross-Zagier

2022/04/22 by Jan Hendrik Bruinier, Bruinier, Jan H., Yingkun Li +3 · 3 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.2204.10604

Abstract

In this paper, we complete the proof of the conjecture of Gross and Zagier concerning algebraicity of higher Green functions at a single CM point on the product of modular curves. The new ingredient is an analogue of the incoherent Eisenstein series over a real quadratic field, which is constructed as the Doi-Naganuma theta lift of a deformed theta integral on hyperbolic space.

Cited by

• A regularized theta lift on the symmetric space of SL_N
• p-adic Higher Green's Functions for Stark-Heegner Cycles
• A note on higher Green's functions

Related

• Traces of CM values of modular functions
• Arithmetic Hirzebruch-Zagier divisors and central derivative values of Rankin-Selberg L-functions
• On a Divisor Modular Form and a Theta Lift
• Special values of Green's functions on hyperbolic 3-space
• A note on higher Green's functions