• M N Huxley

      Articles written in Proceedings – Mathematical Sciences

    • The area within a curve

      M N Huxley

      More Details Abstract Fulltext PDF

      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.

    • The number of ideals in a quadratic field

      M N Huxley N Watt

      More Details Abstract Fulltext PDF

      LetK be a quadratic Geld, and letR(N) be the number of integer ideals inK with norm at most AT. Letx with conductork be the quadratic character associated withK. Then |R(N)−NL(1,x)|⩽Bk50/73N23/73(logN)461/146 forNAk, whereA andB are constants. ForNAkc,C sufficiently large, the factork50/73 may be replaced by (d(k))4/73k46/73.

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