Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014, Article ID 943794, 10 pages
http://dx.doi.org/10.1155/2014/943794
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.

Linked References

  1. R. K. Guy, Unsolved Problems in Number Theory, Springer, New York, NY, USA, 1994.
  2. W. P. Zhang, “A problem of D.H. Lehmer and its Generalization (II),” Compositio Mathematica, vol. 91, pp. 47–56, 1994. View at Google Scholar
  3. W. P. Zhang, “A problem of D.H. Lehmer and its mean square value formula,” Japanese Journal of Mathematics, vol. 29, pp. 109–116, 2003. View at Google Scholar
  4. W. Zhang, X. Zongben, and Y. Yuan, “A problem of D.H. Lehmer and its mean square value formula,” Journal of Number Theory, vol. 103, no. 2, pp. 197–213, 2003. View at Publisher · View at Google Scholar · View at Scopus
  5. Z. Xu and W. Zhang, “On a problem of D.H. Lehmer over short intervals,” Journal of Mathematical Analysis and Applications, vol. 320, no. 2, pp. 756–770, 2006. View at Publisher · View at Google Scholar · View at Scopus
  6. Z. F. Xu and T. P. Zhang, “High-dimensional D. H. Lehmer problem over short intervals,” Acta Mathematica Sinica, vol. 30, pp. 213–228, 2014. View at Google Scholar
  7. Berndt and C. Bruce, “Classical theorems on quadratic residues,” L'Enseignement Mathématique, vol. 22, pp. 261–304, 1976. View at Google Scholar
  8. G. L. Ren and W. P. Zhang, “On the mean value of a sum analogous to character sums over short intervals,” Czechoslovak Mathematical Journal, vol. 133, pp. 651–668, 2008. View at Google Scholar
  9. X. Zhefeng and Z. Wenpeng, “On the order of the high-dimensional Cochrane sum and its mean value,” Journal of Number Theory, vol. 117, no. 1, pp. 131–145, 2006. View at Publisher · View at Google Scholar · View at Scopus
  10. Z. Wenpeng, “On a Cochrane sum and its hybrid mean value formula,” Journal of Mathematical Analysis and Applications, vol. 267, no. 1, pp. 89–96, 2002. View at Publisher · View at Google Scholar · View at Scopus
  11. Z. Xu, “Mean value of the character sums over interval [1, q/8),” Taiwanese Journal of Mathematics, vol. 13, no. 1, pp. 169–187, 2009. View at Google Scholar · View at Scopus