Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A note on the $ 2k$-th power mean of character sums over the quarter interval


Author: Zhefeng Xu
Journal: Proc. Amer. Math. Soc. 136 (2008), 4175-4184
MSC (2000): Primary 11L40, 11L10; Secondary 11M38
DOI: https://doi.org/10.1090/S0002-9939-08-09639-1
Published electronically: July 30, 2008
MathSciNet review: 2431030
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We obtain an asymptotic formula for the $ 2k$-th power mean of odd primitive character sums over the interval $ [1, \frac{q}{4})$.


References [Enhancements On Off] (What's this?)

  • 1. G. Pólya, Über die Verteilung der quadratische Reste und Nichtreste, Göttingen Nachrichten, 1918, pp. 21-29.
  • 2. I. M. Vinogradov, On the distribution of residues and non-residues of powers, Journal of the Physico-Mathematical Society of Perm. 1 (1918), 94-96.
  • 3. A. V. Sokolovski{\v{\i\/}}\kern.15em, On a theorem of Sárkozy, Acta Arithmetica 41 (1982), 27-31. MR 667707 (84e:10046)
  • 4. M. Z. Garaev and A. A. Karatsuba, On character sums and the exceptional set of a congruence problem, Journal of Number Theory 114 (2005), 182-192. MR 2163912 (2006f:11095)
  • 5. D. A. Burgess, Mean value of character sums. II, Mathematika 33 (1987), 1-7. MR 908834 (89g:11072)
  • 6. Zhefeng Xu and Wenpeng Zhang, On the $ 2k$th power mean of the character sums over short intervals, Acta Arithmetica 121 (2006), 149-160. MR 2216139 (2006m:11122)
  • 7. Tom M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, New York, 1976. MR 0434929 (55:7892)
  • 8. Wenpeng Zhang, Yuan Yi and Xiali He, On the $ 2k$-th power mean of Dirichlet L-functions with the weight of general Kloosterman sums, Journal of Number Theory 84 (2000), 199-213. MR 1795790 (2002e:11115)
  • 9. Chengdong Pan and Chengbiao Pan, Element of Analytic Number Theory, Science Press, Beijing, 1999, pp. 95.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11L40, 11L10, 11M38

Retrieve articles in all journals with MSC (2000): 11L40, 11L10, 11M38


Additional Information

Zhefeng Xu
Affiliation: Department of Mathematics, Northwest University, Xi’an, Shaanxi, People’s Republic of China
Email: zhefengxu@hotmail.com; zfxu@nwu.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-08-09639-1
Keywords: Odd primitive character sums, quarter interval, mean value, asymptotic formula
Received by editor(s): November 8, 2007
Published electronically: July 30, 2008
Additional Notes: The author was supported by NSF(10671155) of the People’s Republic of China
Communicated by: Wen-Ching Winnie Li
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society