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<p>Let <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11139_2025_1058_Article_IEq1.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="47" /> </InlineMediaObject> <EquationSource Format="TEX">\(m&gt;1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>m</mi> <mo>&gt;</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> be a square-free integer such that each prime divisor of <i>m</i> is congruent to 3 modulo 4. We show that there is no imaginary cyclic quartic number field whose class number is <i>m</i>. Additionally, we show that this result also holds for certain types of cyclotomic fields.</p>

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Determination of class numbers of imaginary cyclic quartic number fields and cyclotomic fields

  • 期刊论文

  • 发表日期：

    2025年3月17日

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  • Mahesh Kumar Ram

摘要

Let \(m>1\) m > 1 be a square-free integer such that each prime divisor of m is congruent to 3 modulo 4. We show that there is no imaginary cyclic quartic number field whose class number is m. Additionally, we show that this result also holds for certain types of cyclotomic fields.