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Integers Represented by Ternary Quadratic Forms

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Women in Numbers Europe III

Part of the book series: Association for Women in Mathematics Series ((AWMS,volume 24))

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Abstract

In the case of the representation of an integer by an indefinite ternary quadratic form, the violation of the integral Hasse principle can be explained via the Brauer-Manin obstruction. In this note, we study the occurrences of this phenomenon for several families of non-diagonal ternary quadratic forms.

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Acknowledgements

This note originated at a WINE3 workshop at Rennes—we thank the organisers Sorina Ionica, Holly Krieger and Elisa Lorenzo Garcia for creating this opportunity. Moreover, we thank the anonymous referee’s for their careful reading of this manuscript and valuable comments. L.M. is supported by the Swedish Research Council Grant No. 2016-05198 and by a prize of the Göran Gustafsson Foundation. D. S. was supported by a NWO grant 016.Veni.173.016M. M. T. was supported by Czech Science Foundation (GAČR), grant 17-04703Y, by the Charles University, project GA UK No. 1298218, by Charles University Research Centre program UNCE/SCI/022, by project PRIMUS/20/SCI/002, and by the project SVV-2017-260456. K. Z. was supported by DFG project HO 4784/2-1.

Author information

Authors and Affiliations

  1. Université Gaston-Berger de Saint-Louis, Saint Louis, Senegal

    Bernadette Faye

  2. KTH, Department of Mathematics, Stockholm, Sweden

    Lilian Matthiesen

  3. Mathematisches Instituut, Universität Göttingen, Göttingen, Germany

    Damaris Schindler

  4. Faculty of Mathematics and Physics, Department of Algebra, Charles University, Prague, Czech Republic

    Magdaléna Tinková

  5. Fakultät für Mathematik, Technische Universität Dortmund, Dortmund, Germany

    Kristýna Zemková

Authors
  1. Bernadette Faye
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  2. Lilian Matthiesen
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  3. Damaris Schindler
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  4. Magdaléna Tinková
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  5. Kristýna Zemková
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Corresponding author

Correspondence to Damaris Schindler .

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Editors and Affiliations

  1. Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, USA

    Alina Carmen Cojocaru

  2. Laboratoire MIS, University of Picardie Jules Verne, Amiens, France

    Sorina Ionica

  3. Laboratoire IRMAR, Université de Rennes 1, Rennes, France

    Elisa Lorenzo García

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Faye, B., Matthiesen, L., Schindler, D., Tinková, M., Zemková, K. (2021). Integers Represented by Ternary Quadratic Forms. In: Cojocaru, A.C., Ionica, S., García, E.L. (eds) Women in Numbers Europe III. Association for Women in Mathematics Series, vol 24. Springer, Cham. https://doi.org/10.1007/978-3-030-77700-5_7

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