Skip to main content
SpringerLink
Log in

Extension of the Notion of Mahler Measure to a Certain Class of Holomorphic Functions: Properties and Applications

  • Published:
Results in Mathematics Aims and scope Submit manuscript

Abstract

This article is concerned with the asymptotic behaviour of the Mahler measure (defined for the occasion) of functions of the form \(z^n + f(z)\), where f(z) is a holomorphic function on an open subset of \({\mathbb {C}}\) such that \(f(0) \ne 0\).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Jensen, J.L.V.W.: Sur un nouvel et important théorème de la théorie des fonctions. Acta Math. 22, 359–364 (1899)

    Article  MathSciNet  MATH  Google Scholar 

  2. Kronecker, L.: Zwei Sätze über Gleichungen mit ganzzahligen Coefficienten. J. Reine Angew. Math. 53, 173–175 (1857)

    Article  MathSciNet  Google Scholar 

  3. Smyth, C.J.: On the product of the conjugates outside the unit circle of an algebraic integer. Bull. Lond. Math. Soc. 3, 169–175 (1971). MR 44:6641

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Science, Beirut Arab University, P.O. Box 11-5020, Beirut, Lebanon

    T. El Arwadi

  2. IECL, Université de Lorraine, Metz, France

    V. Flammang, G. Rhin & J.-M. Sac-Épée

Authors
  1. T. El Arwadi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. Flammang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. Rhin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. J.-M. Sac-Épée
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J.-M. Sac-Épée.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

El Arwadi, T., Flammang, V., Rhin, G. et al. Extension of the Notion of Mahler Measure to a Certain Class of Holomorphic Functions: Properties and Applications. Results Math 72, 787–791 (2017). https://doi.org/10.1007/s00025-017-0718-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00025-017-0718-0

Mathematics Subject Classification

Search

Navigation