The Ramanujan Journal

, Volume 48, Issue 1, pp 151–157 | Cite as

Universal quadratic forms over multiquadratic fields

  • Vítězslav KalaEmail author
  • Josef Svoboda


For all positive integers k and N, we prove that there are infinitely many totally real multiquadratic fields K of degree \(2^k\) over \(\mathbb {Q}\) such that each universal quadratic form over K has at least N variables.


Universal quadratic form Multiquadratic number field Additively indecomposable integer 

Mathematics Subject Classification

11E12 11R20 



We wish to thank the anonymous referees for a careful reading of the manuscript and for several very helpful comments and corrections.


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of Algebra, Faculty of Mathematics and PhysicsCharles UniversityPraha 8Czech Republic
  2. 2.Mathematisches InstitutUniversity of GöttingenGöttingenGermany

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