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ISSN 1088-6826(e) ISSN 0002-9939(p)

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

Author(s): Zhefeng Xu
Journal: Proc. Amer. Math. Soc. 136 (2008), 4175-4184.
MSC (2000): Primary 11L40, 11L10; Secondary 11M38
Posted: July 30, 2008
MathSciNet review: 2431030
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Abstract | References | Similar articles | Additional information

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

References:

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 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 -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.

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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: 10.1090/S0002-9939-08-09639-1
PII: S 0002-9939(08)09639-1
Keywords: Odd primitive character sums, quarter interval, mean value, asymptotic formula
Received by editor(s): November 8, 2007
Posted: 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
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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