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Class number parities of compositum of quadratic function fields

  • Sunghan Bae and Hwanyup Jung EMAIL logo
Published/Copyright: April 28, 2017
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Abstract

The parities of ideal class numbers of compositum of quadratic function fields are studied. Especially, the parities of ideal class numbers of Fq(t)(P,Q) and Fq(t)(P,Q,R) are completely determined in detail, where P,Q,R are monic irreducible polynomials of even degrees.


This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government(MSIP)(No. 2014001824).



(Communicated by Federico Pellarin)


Acknowledgement

The authors are enormously grateful to the anonymous referee whose comments and suggestions lead to a large improvement of the paper.

References

[1] Bulant, M.: On the parity of the class number of the field Q(p,q,r), J. Number Theory 68 (1998), 72–86.10.1006/jnth.1997.2190Search in Google Scholar

[2] Conner, P. E.—Hurrelbrink, J.: Class Number Parity. Series in Pure Mathematics, Vol. 8, World Scientific, 1988.10.1142/0663Search in Google Scholar

[3] Fröhlich, A.: Central Extensions, Galois Groups and Ideal Class Groups of Number Fields. Contemp. Math., Vol. 24, Amer. Math. Soc., 1983.10.1090/conm/024Search in Google Scholar

[4] Hayes, D. R.: Stickelberger elements in function fields, Compos. Math. 55 (1985), 209–239.Search in Google Scholar

[5] Kučera, R.: On the Stickelberger ideal and circular units of a compositum of quadratic fields, J. Number Theory 56 (1996), 139–166.10.1006/jnth.1996.0008Search in Google Scholar

[6] Kučera, R.: On the parity of the class number of a biquadratic field. J. Number Theory 52 (1995), 43–52.10.1006/jnth.1995.1054Search in Google Scholar

[7] Mouhib, A.: On the parity of the class number of multiquadratic number fields. J. Number Theory 129 (2009), 1205–1211.10.1016/j.jnt.2008.12.013Search in Google Scholar

[8] Rosen, M.: Number Theory in Function Fields, GTM No. 210, Springer, 2001.10.1007/978-1-4757-6046-0Search in Google Scholar

Received: 2014-5-26
Accepted: 2014-11-25
Published Online: 2017-4-28
Published in Print: 2017-4-25

© 2017 Mathematical Institute Slovak Academy of Sciences

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