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<p>We establish an effective version of Siegel’s lower bounds for class numbers of imaginary quadratic fields in certain curves in <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(Y(1)^n\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>Y</mi> <msup> <mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> <mi>n</mi> </msup> </mrow> </math></EquationSource> </InlineEquation>. Our proof goes through the G-functions method of Yves André. Following recent results of G. Binyamini, these lead to effective André–Oort statements for the curves in question.</p>

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Effective Brauer–Siegel on some curves in \(Y(1)^n\)

  • 期刊论文

  • 发表日期：

    2026年3月2日

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  • Georgios Papas

摘要

We establish an effective version of Siegel’s lower bounds for class numbers of imaginary quadratic fields in certain curves in \(Y(1)^n\) Y ( 1 ) n . Our proof goes through the G-functions method of Yves André. Following recent results of G. Binyamini, these lead to effective André–Oort statements for the curves in question.