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Abstract and Applied Analysis
Volume 2014, Article ID 943794, 10 pages
Research Article

High-Dimensional D. H. Lehmer Problem over Quarter Intervals

College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710119, China

Received 9 January 2014; Accepted 31 March 2014; Published 24 April 2014

Academic Editor: Soon-Yeong Chung

Copyright © 2014 Tianping Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The high-dimensional D. H. Lehmer problem over quarter intervals is studied. By using the properties of character sum and the estimates of Dirichlet -function, the previous result is improved to be the best possible in the case of , an odd prime with (mod 4), which is shown by studying the mean square value of the error term.