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Integer points in a domain with smooth boundary

  • M. N. Huxley
Part of the Progress in Mathematics book series (PM, volume 102)

Abstract

In the earlier paper [8] we discussed the method of estimating the area A of a domain Ω in the Euclidean plane by counting squares. A piece of transparent squared paper (with M squares per unit length, say) is placed over the domain. One counts either
  1. Q1:

    the number of squares whose centre lies within Ω or on its boundary C, or

     
  2. Q2:

    the number of vertices of the square lattice which lie within Ω or on C, or

     
  3. Q3:

    the number of squares which lie wholly within Ω plus half the number of squares cut by C.

     

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Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • M. N. Huxley
    • 1
  1. 1.School of MathematicsUniversity of Wales College of CardiffCardiffUK

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