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PreprintarXiv licencearXiv

On The Manin Constant

  • Zhuoni Chi
  • Shurui Liu
  • Ping Nie
Open at sourcePDFDOICite

Abstract

We prove the Manin constant conjecture for every optimal elliptic curve over ℚ and Stevens' Conjectures I and II. Our method adapts Hongbo Yin's congruence argument for cubic roots of modular functions to lifts of modular parametrizations through isogenies, using the unbounded denominators theorem of Calegari, Dimitrov and Tang.

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Cite

BibTeXRIS
BibTeX
@misc{chi2026manin,
  title = {{On The Manin Constant}},
  author = {Zhuoni Chi and Shurui Liu and Ping Nie},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25672},
  eprint = {2610.25672},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25672},
}
RIS
TY  - UNPB
TI  - On The Manin Constant
AU  - Zhuoni Chi
AU  - Shurui Liu
AU  - Ping Nie
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.25672
UR  - https://arxiv.org/abs/2610.25672
AB  - We prove the Manin constant conjecture for every optimal elliptic curve over ℚ and Stevens' Conjectures I and II. Our method adapts Hongbo Yin's congruence argument for cubic roots of modular functions to lifts of modular parametrizations through isogenies, using the unbounded denominators theorem of Calegari, Dimitrov and Tang.
ER  -