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The area within a curve

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Abstract

The area of a simple closed convex curve can be estimated in terms of the number of points of a square lattice that lie within the curve. We obtain the usual error bound without integration using a form of the Hardy—Littlewood—Ramanujan circle method, and also present simple estimates for the mean square error.

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References

  1. Bombieri E and Iwaniec H, On the order of (1/2 + it),Ann. Scuola Normale Superiore di Pisa cl. Sci. (4)13(1986)449–472

    MATH  MathSciNet  Google Scholar 

  2. Hardy G H and Ramanujan S, Asymptotic formulae in combinatory analysis,Proc. London Math. Soc. 217 (1918) 75–115

    Article  Google Scholar 

  3. Huxley M N and Watt N, Exponential sums and the Riemann zeta functionProc. London Math. Soc. (to appear)

  4. Huxley M N, Exponential sums and lattice points (to appear)

  5. Iwaniec H and Mozzochi C J, On the circle and divisor problems (to appear)

  6. Jutila M,Lectures on a method in the theory of exponential sums (Bombay: Tata Institute of Fundamental Research) (1987)

    MATH  Google Scholar 

  7. Landau E,Vorlesunaen über Zahlentheorie (Leipzig: Hirzel) Band 2 (1927)

    Google Scholar 

  8. Sierpin’ski W, A certain problem in the calculus of asymptotic functions,Prace Mat.-Fiz. 17 (1906) 77–118 andOeuvres Choisies 73–108

    Google Scholar 

  9. Swinnerton-Dyer H P F, The number of lattice points on a convex curve,J. Number Theory 6 (1974) 128–135

    Article  MATH  MathSciNet  Google Scholar 

  10. Vinogradov I M,An introduction to the theory of numbers (Oxford: Pergamon) (1955)

    Google Scholar 

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Authors and Affiliations

  1. Department of Pure Mathematics, University College, Cardiff, PO Box 78, CF1 1XL, Cardiff, UK

    M. N. Huxley

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  1. M. N. Huxley
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Huxley, M.N. The area within a curve. Proc. Indian Acad. Sci. (Math. Sci.) 97, 111–116 (1987). https://doi.org/10.1007/BF02837818

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  • DOI: https://doi.org/10.1007/BF02837818

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