On the mean value of a sum analogous to character sums over short intervals

Ren Ganglian; Zhang Wenpeng

Czechoslovak Mathematical Journal (2008)

  • Volume: 58, Issue: 3, page 651-668
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Ganglian, Ren, and Wenpeng, Zhang. "On the mean value of a sum analogous to character sums over short intervals." Czechoslovak Mathematical Journal 58.3 (2008): 651-668. <http://eudml.org/doc/37858>.

@article{Ganglian2008,
abstract = {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.},
author = {Ganglian, Ren, Wenpeng, Zhang},
journal = {Czechoslovak Mathematical Journal},
keywords = {character sums; short intervals; even power mean; asymptotic formula; character sums; short intervals; even power mean; asymptotic formula},
language = {eng},
number = {3},
pages = {651-668},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the mean value of a sum analogous to character sums over short intervals},
url = {http://eudml.org/doc/37858},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Ganglian, Ren
AU - Wenpeng, Zhang
TI - On the mean value of a sum analogous to character sums over short intervals
JO - Czechoslovak Mathematical Journal
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 3
SP - 651
EP - 668
AB - 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.
LA - eng
KW - character sums; short intervals; even power mean; asymptotic formula; character sums; short intervals; even power mean; asymptotic formula
UR - http://eudml.org/doc/37858
ER -

References

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  1. Pólya, G., Über die Verteilung der quadratische Reste und Nichtreste, Göttingen Nachrichten (1918), 21-29. (1918) 
  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. (1918) 
  3. Sokolovskiĭ, A. V., On a theorem of Sárkozy, Acta Arithmetica 41 (1982), 27-31. (1982) MR0667707
  4. Burgess, D. A., 10.4064/aa-27-1-265-267, Acta Arithmetica 27 (1975), 265-267. (1975) Zbl0258.10018MR0364125DOI10.4064/aa-27-1-265-267
  5. Xu, Zhefeng, Zhang, Wenpeng, 10.4064/aa121-2-4, Acta Arithmetica 121 (2006), 149-160. (2006) Zbl1153.11046MR2216139DOI10.4064/aa121-2-4
  6. Peral, Juan C., 10.1090/conm/189/02280, Contemporary Mathematics 189 (1995), 449-459. (1995) Zbl0837.11045MR1347030DOI10.1090/conm/189/02280
  7. Zhang, Wenpeng, 10.1016/S0022-247X(02)00501-2, Journal of Mathematical Analysis and Applications 276 (2002), 446-457. (2002) Zbl1106.11304MR1944361DOI10.1016/S0022-247X(02)00501-2
  8. Zhang, Wenpeng, Yi, Yuan, He, Xiali, 10.1006/jnth.2000.2515, Journal of Number Theory 84 (2000), 199-213. (2000) Zbl0958.11061MR1795790DOI10.1006/jnth.2000.2515
  9. He, Xiali, Zhang, Wenpeng, 10.1007/BF02650668, Acta Mathematica 15 (1999), 245-254. (1999) MR1714067DOI10.1007/BF02650668

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