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NON-PÓLYA FIELDS WITH LARGE PÓLYA GROUPS ARISING FROM LEHMER QUINTICS

Part of: Algebraic number theory: global fields

Published online by Cambridge University Press:  11 March 2024

NIMISH KUMAR MAHAPATRA Open the ORCID record for NIMISH KUMAR MAHAPATRA [Opens in a new window]  and
PREM PRAKASH PANDEY Open the ORCID record for PREM PRAKASH PANDEY [Opens in a new window]
NIMISH KUMAR MAHAPATRA*
Affiliation:
Department of Mathematical Sciences, Indian Institute of Science Education and Research, Berhampur, India
PREM PRAKASH PANDEY
Affiliation:
Department of Mathematical Sciences, Indian Institute of Science Education and Research, Berhampur, India e-mail: premp@iiserbpr.ac.in
*
e-mail: nimishkm18@iiserbpr.ac.in
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Abstract

We construct a new family of quintic non-Pólya fields with large Pólya groups. We show that the Pólya number of such a field never exceeds five times the size of its Pólya group. Finally, we show that these non-Pólya fields are nonmonogenic of field index one.

Keywords

Pólya fieldPólya groupHilbert class fieldgenus field

MSC classification

Primary: 11R29: Class numbers, class groups, discriminants
Secondary: 11R04: Algebraic numbers; rings of algebraic integers 11R20: Other abelian and metabelian extensions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , First View , pp. 1 - 12
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

N.K.M. would like to acknowledge financial support from the University Grants Commission (UGC), Government of India.

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