Skip to main content

Some metric results in Transcendental Numbers Theory

  • 1034 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 1752)

Abstract

In this Chapter we describe some results in the metric theory of transcendental numbers. Let begin with some notation. If P ∈ Z[x[inl, ⋯, x m] is a non - zero polynomial, we define its size t(P) as h(P) + deg (P). Here, h(P) is the Weil’s logarithmic height of P (so, if the ged of the coefficients of P is 1, then h(P) is the logarithm of the maximum module of the coefficients of P) and deg (P) is the total degree of P. Let α = (α1,⋯, αm) ∈ Cm with α1,⋯, αm algebraically dependent: we define t(α) as the minimum size of a non - zero polynomial P ∈ Z[x l⋯,x m] such that P(α) = 0. er’s author : Francesco AMOROSO.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

(2001). Some metric results in Transcendental Numbers Theory. In: Nesterenko, Y.V., Philippon, P. (eds) Introduction to Algebraic Independence Theory. Lecture Notes in Mathematics, vol 1752. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44550-1_15

Download citation

  • DOI: https://doi.org/10.1007/3-540-44550-1_15

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41496-4

  • Online ISBN: 978-3-540-44550-0

  • eBook Packages: Springer Book Archive