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Norm form equations with solutions taking values in a multi-recurrence

Volume 198 / 2021

Clemens Fuchs, Sebastian Heintze Acta Arithmetica 198 (2021), 427-438 MSC: 11D57, 11B37, 11J87. DOI: 10.4064/aa200622-22-10 Published online: 8 February 2021

Abstract

We are interested in solutions of a norm form equation that takes values in a given multi-recurrence. We show that among the solutions there are only finitely many different values in each component which lie in the given multi-recurrence unless the recurrence is of a precisely described exceptional shape. This gives a variant of the question on arithmetic progressions in the solution set of norm form equations.

Authors

  • Clemens FuchsDepartment of Mathematics
    University of Salzburg
    Hellbrunnerstr. 34
    5020 Salzburg, Austria
    e-mail
  • Sebastian HeintzeDepartment of Mathematics
    University of Salzburg
    Hellbrunnerstr. 34
    5020 Salzburg, Austria
    e-mail

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