Publikationsdetails
Some uniform effective results on André
Oort for sums of powers in ℂ^n
Abstract
We prove an André-Oort-type result for a family of hypersurfaces in Cn that is both uniform and effective. Let K*denote the single exceptional imaginary quadratic field which occurs in the Siegel-Tatuzawa lower bound for the class number. We prove that, for m, n ∈ Z>0, there exists an effective constant c(m, n)>0 with the following property: if pairwise distinct singular moduli x1, . . . , xn with respective discriminants Δ1, . . . , Δn are such that a1xm 1 + + anxm n ∈ Q for some a1, . . . , an ∈ Q \ {0} and #{Δi : Q( √ Δi) =K*} ≤ 1, then maxi|Δi| ≤ c(m, n). In addition, we prove an unconditional and completely explicit version of this result when (m, n)=(1, 3) and thereby determine all the triples (x1, x2, x3) of singular moduli such that a1x1 +a2x2 +a3x3 ∈ Q for some a1, a2, a3 ∈ Q \ {0}.
Details
- Externe Organisation(en)
-
University of Manchester
- Typ
- Artikel
- Journal
- Mathematical Proceedings of the Cambridge Philosophical Society
- Band
- 180
- Seiten
- 607-641
- Anzahl der Seiten
- 35
- ISSN
- 0305-0041
- Publikationsdatum
- 01.05.2026
- Publikationsstatus
- Veröffentlicht
- Peer-reviewed
- Ja
- ASJC Scopus Sachgebiete
- Allgemeine Mathematik
- Elektronische Version(en)
-
https://doi.org/10.1017/S0305004125101825 (Zugang:
Offen
)
https://doi.org/10.48550/arXiv.2405.06456 (Zugang: Offen )
