Previous |  Up |  Next

Article

Keywords:
character sums; short intervals; even power mean; asymptotic formula
Summary:
The main purpose of this paper is to study the mean value properties of a sum analogous to character sums over short intervals by using the mean value theorems for the Dirichlet L-functions, and to give some interesting asymptotic formulae.
References:
[1] Pólya, G.: Über die Verteilung der quadratische Reste und Nichtreste. Göttingen Nachrichten (1918), 21-29.
[2] Vinogradov, I. M.: On the distribution of residues and non-residues of powers. Journal of the Physico-Mathematical society of Perm 1 (1918), 94-96.
[3] Sokolovskiĭ, A. V.: On a theorem of Sárkozy. Acta Arithmetica 41 (1982), 27-31. MR 0667707
[4] Burgess, D. A.: On a conjecture of Norton. Acta Arithmetica 27 (1975), 265-267. MR 0364125 | Zbl 0258.10018
[5] Xu, Zhefeng, Zhang, Wenpeng: On the $2k$th power mean of the character sums over short intervals. Acta Arithmetica 121 (2006), 149-160. DOI 10.4064/aa121-2-4 | MR 2216139 | Zbl 1153.11046
[6] Peral, Juan C.: Character sums and explicit estimates for L-functions. Contemporary Mathematics 189 (1995), 449-459. DOI 10.1090/conm/189/02280 | MR 1347030 | Zbl 0837.11045
[7] Zhang, Wenpeng: On a Cochrane sum and its hybrid mean value formula (II). Journal of Mathematical Analysis and Applications 276 (2002), 446-457. DOI 10.1016/S0022-247X(02)00501-2 | MR 1944361 | Zbl 1106.11304
[8] Zhang, Wenpeng, Yi, Yuan, 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. DOI 10.1006/jnth.2000.2515 | MR 1795790 | Zbl 0958.11061
[9] He, Xiali, Zhang, Wenpeng: On the mean value of Dedekind sums. Acta Mathematica 15 (1999), 245-254. DOI 10.1007/BF02650668 | MR 1714067
Partner of
EuDML logo