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Archiv der Mathematik

, Volume 97, Issue 5, pp 413–421 | Cite as

Capitulation problem for global function fields

  • Yan Li
  • Su Hu
Article

Abstract

Let q be a power of an odd prime number \({p, k=\mathbb{F}_{q}(t)}\) be the rational function field over the finite field \({\mathbb{F}_{q}.}\) In this paper, we construct infinitely many real (resp. imaginary) quadratic extensions K over k whose ideal class group capitulates in a proper subfield of the Hilbert class field of K. The proof of the infinity of such fields K relies on an estimation of certain character sum over finite fields.

Mathematics Subject Classification (2010)

Primary 11R58 Secondary 11A15 11R37 

Keywords

Quadratic function field Hilbert class field Genus field Ideal class group Capitulation problem 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Department of Applied MathematicsChina Agriculture UniversityBeijingChina
  2. 2.Department of Mathematical SciencesKorea Advanced Institute of Science and Technology (KAIST)DaejeonSouth Korea

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