Pith. sign in

REVIEW 2 cited by

Deformations of Theta Integrals and A Conjecture of Gross-Zagier

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2204.10604 v3 pith:NM66SDOB submitted 2022-04-22 math.NT

Jan H. Bruinier , Yingkun Li , Tonghai Yang This is my paper · ORCID
classification math.NT
keywords thetaconjecturealgebraicityanaloguecompleteconcerningconstructedcurves
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original 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.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Twisted Siegel-Weil formulas for $\mathrm{GL}_2$ over non-Galois quartic CM fields

    math.NT 2026-07 conditional novelty 7.0 of 10

    Twisted theta integrals over non-Galois quartic CM fields equal Doi–Naganuma lifts of Hecke's integral, making twisted CM values of Borcherds forms algebraic multiples of logarithms of units.

  2. Hilbert Eisenstein series as Doi-Naganuma lift

    math.NT 2025-06 conditional novelty 7.0 of 10

    Incoherent Hilbert Eisenstein series over real quadratic fields are realized as Doi-Naganuma theta lifts, yielding explicit Rankin-Selberg L-functions and a non-unit theorem for Borcherds products at CM points.

Pith tools