A class number problem for imaginary cyclic number fields of 2-power degrees

In 2024, M. K. Ram proved that the class number of an imaginary cyclic quartic number field is never equal to a prime $p\equiv 3\pmod 4$. Here we greatly generalize this result to the case of the non-quadratic imaginary cyclic number fields of $2$-power degrees and not necessarily prime class numbers.

Publication Details

Journal
ArXiv.org
Published
2025-08-14
Primary Topic
Algebraic Geometry and Number Theory
Type
article
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article

A class number problem for imaginary cyclic number fields of 2-power degrees

ArXiv.org
Algebraic Geometry and Number Theory
article

A class number problem for imaginary cyclic number fields of 2-power degrees

article en

Abstract

In 2024, M. K. Ram proved that the class number of an imaginary cyclic quartic number field is never equal to a prime $p\equiv 3\pmod 4$. Here we greatly generalize this result to the case of the non-quadratic imaginary cyclic number fields of $2$-power degrees and not necessarily prime class numbers.

ArXiv.org
Reduced inequalities
Openalex Percentile: Top 44%
Algebraic Geometry and Number Theory
Open Access PDFOpenAlex
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A class number problem for imaginary cyclic number fields of 2-power degrees · ArXiv.org (2025) | TGRS Research Map | TGRS