Integer points close to a smooth curve
by
Ognian Trifonov
University of South Carolina

Huxley and T. proved recently that the interval (x , x+h] contains the "right" number of squarefull integers namely [(\zeta(3/2))/(2\zeta(3))] x^\theta (1+o(1)) when h = x^{1/2 + \theta}, \theta > 1/8 and x is sufficiently large. To prove this result estimates for the number of integer points close to a certain smooth curve are needed. We improve on these estimates and as a result we extend the range of admissible values for \theta below 1/8.

Date received: April 13, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacu-07.