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On the height of solutions to norm form equations

Volume 183 / 2018

Shabnam Akhtari, Jeffrey D. Vaaler Acta Arithmetica 183 (2018), 385-396 MSC: 11J25, 11R27, 11S20. DOI: 10.4064/aa170907-18-2 Published online: 9 April 2018

Abstract

Let $k$ be a number field. We consider norm form equations associated to a full $O_k$-module contained in a finite extension field $l$. It is known that the set of solutions is naturally a union of disjoint equivalence classes of solutions. We prove that each nonempty equivalence class of solutions contains a representative with Weil height bounded by an expression that depends on parameters defining the norm form equation.

Authors

  • Shabnam AkhtariDepartment of Mathematics
    University of Oregon
    Eugene, OR 97402, U.S.A.
    e-mail
  • Jeffrey D. VaalerDepartment of Mathematics
    University of Texas
    Austin, TX 78712, U.S.A.
    e-mail

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