Taiwanese Journal of Mathematics

MEAN VALUE OF THE CHARACTER SUMS OVER INTERVAL

Zhefeng Xu

Full-text: Open access

Abstract

Let $q\gt 8$ be an odd integer and $p$ a prime with $p$ a prime with $p\lt q$ and $p\nmid q$. The main purpose of this paper is to study the mean value properties of the character sums over interval $\left[1, \frac{q}{8}\right)$ by using the mean value theorems of the Dirichlet L-functions,and give some interesting mean value formulae.

Article information

Source
Taiwanese J. Math., Volume 13, Number 1 (2009), 169-187.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405277

Digital Object Identifier
doi:10.11650/twjm/1500405277

Mathematical Reviews number (MathSciNet)
MR2489312

Zentralblatt MATH identifier
1196.11115

Subjects
Primary: 11L40: Estimates on character sums

Keywords
haracter sums mean value asymptotic formula

Citation

Xu, Zhefeng. MEAN VALUE OF THE CHARACTER SUMS OVER INTERVAL. Taiwanese J. Math. 13 (2009), no. 1, 169--187. doi:10.11650/twjm/1500405277. https://projecteuclid.org/euclid.twjm/1500405277


Export citation

References

  • [1.] G. P$\acute{\text{o}}$lya, $\ddot{\text{U}}$ber die Verteilung der quadratische Reste und Nichtreste, G$\ddot{\text{o}}$ttingen Nachrichten, 1918, pp. 21-29.
  • [2.] I. M. Vinogradov, On the diswtribution of residues and non-residues of powers, Journal of the Physico-Mathematical society of Perm., 1 (1918), 94-96.
  • [3.] A. V. Sokolovski$\check{\text{i}}$, On a theorem of S$\acute{\text{a}}$rkozy, Acta Arithmetica, 41 (1982), 27-31.
  • [4.] D. A. Burgess, On a conjecture of Norton, Acta Arithmetica, 27 (1975), 265-267.
  • [5.] K. K. Norton, On character sums and power residues, Trans. Amer. Math. Soc., 167 (1972), 203-226.
  • [6.] D. A. Burgess, Mean value of character sums, Mathematika, 33 (1986), 1-5.
  • [7.] D. A. Burgess, Mean value of character sums II, Mathematika, 33 (1987), 1-7.
  • [8.] H. L. Montgomery and R. C. Vaughan, Mean value of character sums, Canadian Journal of Mathematics, 31(3) (1979), 476-487.
  • [9.] Xu zhefeng and Zhang Wenpeng, On the $2k$th power mean of the character sums over short intervals, Acta Arithmetica, 121, (2006), 149-160.
  • [10.] Juan C. Peral, Character sums and explicit estimates for L-functions, Contemporary Mathematics, 189 (1995), 449-459.
  • [11.] Wenpeng Zhang, On a Cochrane sum and its hybrid mean value formula (II), Journal of Mathematical Analysis and Applications, 276 (2002), 446-457.
  • [12.] Zhang Wenpeng, Yi Yuan and He Xiali, 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.