# An effective result of André-Oort type II

Acta Arithmetica (2013)

- Volume: 161, Issue: 1, page 1-19
- ISSN: 0065-1036

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topLars Kühne. "An effective result of André-Oort type II." Acta Arithmetica 161.1 (2013): 1-19. <http://eudml.org/doc/286622>.

@article{LarsKühne2013,

abstract = {We prove some new effective results of André-Oort type. In particular, we state certain uniform improvements of the main result in [L. Kühne, Ann. of Math. 176 (2012), 651-671]. We also show that the equation X + Y = 1 has no solution in singular moduli. As a by-product, we indicate a simple trick rendering André's proof of the André-Oort conjecture effective. A significantly new aspect is the usage of both the Siegel-Tatuzawa theorem and the weak effective lower bound on the class number of an imaginary quadratic field given by Gross and Zagier. The results of this article were partially announced in the above-cited paper.},

author = {Lars Kühne},

journal = {Acta Arithmetica},

keywords = {André-Oort conjecture; modular curve; effective; uniformity},

language = {eng},

number = {1},

pages = {1-19},

title = {An effective result of André-Oort type II},

url = {http://eudml.org/doc/286622},

volume = {161},

year = {2013},

}

TY - JOUR

AU - Lars Kühne

TI - An effective result of André-Oort type II

JO - Acta Arithmetica

PY - 2013

VL - 161

IS - 1

SP - 1

EP - 19

AB - We prove some new effective results of André-Oort type. In particular, we state certain uniform improvements of the main result in [L. Kühne, Ann. of Math. 176 (2012), 651-671]. We also show that the equation X + Y = 1 has no solution in singular moduli. As a by-product, we indicate a simple trick rendering André's proof of the André-Oort conjecture effective. A significantly new aspect is the usage of both the Siegel-Tatuzawa theorem and the weak effective lower bound on the class number of an imaginary quadratic field given by Gross and Zagier. The results of this article were partially announced in the above-cited paper.

LA - eng

KW - André-Oort conjecture; modular curve; effective; uniformity

UR - http://eudml.org/doc/286622

ER -

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