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Ideal Factorization Method and Its Applications

  • Sibel Kurt
  • Oǧuz Yayla
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 276)

Abstract

In this work the unsolvability of certain equations is studied in the case of cyclotomic number fields whose ring of integers is not a principal ideal domain. Winterhof et al. considered the equations for \(\gamma \in {\mathbb Z}\). We first extend this result to \(\gamma \in {\mathbb R}\cap {\mathbb Z}[\zeta _m]\) by using a new method from algebraic number theory. Then we present its applications to \(\gamma \)-Butson-Hadamard matrices, \(\gamma \)-Conference matrices and type \(\gamma \) nearly perfect sequences for \(\gamma \in {\mathbb R}\cap {\mathbb Z}[\zeta _m] \).

Keywords

Ideal factorization Butson-Hadamard matrices Conference matrices Nearly perfect sequences 

Notes

Acknowledgements

This work was supported by TÜBİTAK (The Scientific and Technological Research Council of Turkey) Project No: 116R026.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsHacettepe UniversityAnkaraTurkey

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