Optimal stretching for lattice points under convex curves

  title={Optimal stretching for lattice points under convex curves},
  author={Sinan Ariturk and Richard S. Laugesen},
Suppose we count the positive integer lattice points beneath a convex decreasing curve in the first quadrant having equal intercepts. Then stretch in the coordinate directions so as to preserve the area under the curve, and again count lattice points. Which choice of stretch factor will maximize the lattice point count? We show the optimal stretch factor approaches 1 as the area approaches infinity. In particular, when 0 < p < 1, among p-ellipses |sx| + |s−1y|p = r with s > 0, the one enclosing… CONTINUE READING

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