Integer Points Close to Smooth Curves
Some number-theoretic problems involve the number of points with integer coordinates very near some smooth plane curves. This chapter introduces the basic results and some refinements of the theory. Some criteria are investigated and the theorem of Huxley and Sargos is studied in detail. In the section Further Developments, we prove a particular case of a general theorem given by Filaseta and Trifonov improving on the distribution of squarefree numbers in short segments. The dual problem of square-full numbers in short intervals is also investigated.
- [Hux99]Huxley MN (1999) The integer points close to a curve III. In: Győry et al. (eds) Number theory in progress, vol 2. de Gruyter, Berlin, pp 911–940 Google Scholar