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Extreme values of central L-derivatives and heights of Heegner points

  • Mohammad H. Hamdar
  • Sun-Kai Leung
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Abstract

Using Soundararajan's resonance method, we obtain extreme values of the central derivatives L(r)(1/2,f⊗χd), where f is a normalized newform and χd ranges over primitive real characters associated with negative fundamental discriminants. The twisted first moment estimate used in the proof may be of independent interest. Applying Gross--Zagier-type formulas, we obtain correspondingly large Néron--Tate heights of Heegner points on elliptic curves and large absolute values of Beilinson--Bloch heights of Heegner cycles attached to modular forms.

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Cite

BibTeXRIS
BibTeX
@misc{hamdar2026extreme,
  title = {{Extreme values of central $L$-derivatives and heights of Heegner points}},
  author = {Mohammad H. Hamdar and Sun-Kai Leung},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.26786},
  eprint = {2609.26786},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.26786},
}
RIS
TY  - UNPB
TI  - Extreme values of central L-derivatives and heights of Heegner points
AU  - Mohammad H. Hamdar
AU  - Sun-Kai Leung
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.26786
UR  - https://arxiv.org/abs/2609.26786
AB  - Using Soundararajan's resonance method, we obtain extreme values of the central derivatives L^(r)(1/2,f⊗χ_d), where f is a normalized newform and χ_d ranges over primitive real characters associated with negative fundamental discriminants. The twisted first moment estimate used in the proof may be of independent interest. Applying Gross--Zagier-type formulas, we obtain correspondingly large Néron--Tate heights of Heegner points on elliptic curves and large absolute values of Beilinson--Bloch heights of Heegner cycles attached to modular forms.
ER  -