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Explicit height bounds on modular polynomials for the elliptic j-invariant, cube root of j, and Weber modular function f

  • Abraham Zhang
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Abstract

We improve an explicit upper bound on the height of the modular polynomial ΦN given by Breuer, Gómez, and Pazuki. We also prove new explicit upper bounds on the height of modular polynomials for the cube root of j and the Weber modular function f.

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Cite

BibTeXRIS
BibTeX
@misc{zhang2026explicit,
  title = {{Explicit height bounds on modular polynomials for the elliptic $j$-invariant, cube root of $j$, and Weber modular function $\mathfrak f$}},
  author = {Abraham Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.22214},
  eprint = {2607.22214},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.22214},
}
RIS
TY  - UNPB
TI  - Explicit height bounds on modular polynomials for the elliptic j-invariant, cube root of j, and Weber modular function f
AU  - Abraham Zhang
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2607.22214
UR  - https://arxiv.org/abs/2607.22214
AB  - We improve an explicit upper bound on the height of the modular polynomial Φ_N given by Breuer, Gómez, and Pazuki. We also prove new explicit upper bounds on the height of modular polynomials for the cube root of j and the Weber modular function f.
ER  -