Skip to main content
SpringerLink
Log in

Index of lattices and Hilbert polynomials

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

An upper bound for the index of a sublattice, which arises in relation to various versions of zero lemmas in the theory of linear forms in logarithms of algebraic numbers, in terms of the Hilbert polynomial is found. Simultaneously, a lower bound for the values of this polynomial is obtained.

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

Bibliography

  1. M. Waldschmidt, Diophantine Approximation on Linear Algebraic Groups, Springer-Verlag, 2000.

  2. T. Loher and D. Masser, “Uniformly counting of bounded height,” Acta Arith., 111 (2004), no. 3, 277–297.

    Article  MATH  MathSciNet  Google Scholar 

  3. E. M. Matveev, “On successive minima of the extended logarithmic height of algebraic numbers,” Mat. Sb. [Math. USSR-Sb.], 190 (1999), no. 3, 89–108.

    MATH  MathSciNet  Google Scholar 

  4. E. M. Matveev, “An explicit lower bound for a homogeneous rational linear form in logarithms of algebraic numbers,” Izv. Ross. Akad. Nauk Ser. Mat. [Russian Acad. Sci. Izv. Math.], 62 (1998), no. 4, 81–136.

    MATH  MathSciNet  Google Scholar 

  5. P. Philippon and M. Waldschmidt, “Lower bounds for linear forms in logarithms,” in: New Advances in Transcendence Theory, ed. A. Baker, Cambridge Univ. Press, Cambridge, 1988, pp. 280–312.

    Google Scholar 

  6. Yu. M. Aleksentsev, The Hilbert Polynomial and Linear Forms in Logarithms of Algebraic Numbers [in Russian] (Manuscript deposited at VINITI on April 4, 2005; deposition no. 515-V2005), 2005.

  7. M. Meyer and A. Pajor, “Sections of the unit ball of l n p ” J. Funct. Anal., 80 (1988), no. 1, 109–123.

    Article  MATH  MathSciNet  Google Scholar 

  8. J. W. S. Cassels, An Introduction to the Geometry of Numbers, Springer-Verlag, Berlin, 1959.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow Institute of Steel and Alloys, Moscow

    Yu. M. Aleksentsev

Authors
  1. Yu. M. Aleksentsev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Matematicheskie Zametki, vol. 80, no. 3, 2006, pp. 323–327.

Original Russian Text Copyright © 2006 by Yu. M. Aleksentsev.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aleksentsev, Y.M. Index of lattices and Hilbert polynomials. Math Notes 80, 313–317 (2006). https://doi.org/10.1007/s11006-006-0142-3

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11006-006-0142-3

Key words

Search

Navigation