On the mean lattice point discrepancy of a convex disc |
| |
Authors: | W G Nowak |
| |
Institution: | Institut für Mathematik u. Ang. Stat., Universit?t für Bodenkultur, Peter Jordan-Stra?e 82,? A-1190 Wien, Austria, e-mail: nowak@mail.boku.ac.at, http://www.boku.ac.at/math/nth.html, AT
|
| |
Abstract: | For a convex planar domain D \cal {D} , with smooth boundary of finite nonzero curvature, we consider the number of lattice points in the linearly dilated domain t D t \cal {D} . In particular the lattice point discrepancy PD(t) P_{\cal {D}}(t) (number of lattice points minus area), is investigated in mean-square over short intervals. We establish an asymptotic formula for¶¶ òT - LT + L(PD(t))2dt \int\limits_{T - \Lambda}^{T + \Lambda}(P_{\cal {D}}(t))^2\textrm{d}t ,¶¶ for any L = L(T) \Lambda = \Lambda(T) growing faster than logT. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|