A hybrid mean value of the Dedekind sums

Hai Yang

Czechoslovak Mathematical Journal (2010)

  • Volume: 60, Issue: 4, page 1055-1063
  • ISSN: 0011-4642

Abstract

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The main purpose of this paper is to use the M. Toyoizumi's important work, the properties of the Dedekind sums and the estimates for character sums to study a hybrid mean value of the Dedekind sums, and give a sharper asymptotic formula for it.

How to cite

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Yang, Hai. "A hybrid mean value of the Dedekind sums." Czechoslovak Mathematical Journal 60.4 (2010): 1055-1063. <http://eudml.org/doc/196534>.

@article{Yang2010,
abstract = {The main purpose of this paper is to use the M. Toyoizumi's important work, the properties of the Dedekind sums and the estimates for character sums to study a hybrid mean value of the Dedekind sums, and give a sharper asymptotic formula for it.},
author = {Yang, Hai},
journal = {Czechoslovak Mathematical Journal},
keywords = {Dedekind sums; Dirichlet $L$-function; mean value; Dedekind sum; Dirichlet -function; mean value},
language = {eng},
number = {4},
pages = {1055-1063},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A hybrid mean value of the Dedekind sums},
url = {http://eudml.org/doc/196534},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Yang, Hai
TI - A hybrid mean value of the Dedekind sums
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 4
SP - 1055
EP - 1063
AB - The main purpose of this paper is to use the M. Toyoizumi's important work, the properties of the Dedekind sums and the estimates for character sums to study a hybrid mean value of the Dedekind sums, and give a sharper asymptotic formula for it.
LA - eng
KW - Dedekind sums; Dirichlet $L$-function; mean value; Dedekind sum; Dirichlet -function; mean value
UR - http://eudml.org/doc/196534
ER -

References

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  1. Carlitz, L., 10.2140/pjm.1953.3.513, Pac. J. Math. 3 (1953), 513-522. (1953) MR0056020DOI10.2140/pjm.1953.3.513
  2. Rademacher, H., On the transformation of log η ( τ ) , J. Indian Math. Soc. 19 (1955), 25-30. (1955) Zbl0064.32703MR0070660
  3. Mordell, L. J., 10.2307/2372310, Am. J. Math. 73 (1951), 593-598. (1951) Zbl0042.27401MR0042449DOI10.2307/2372310
  4. Conrey, J. B., Fransen, E., Klein, R., Scott, C., 10.1006/jnth.1996.0014, J. Number Theory 56 (1996), 214-226. (1996) Zbl0851.11028MR1373548DOI10.1006/jnth.1996.0014
  5. Walum, H., An exact formula for an average of L -series, Il. J. Math. 26 (1982), 1-3. (1982) Zbl0464.10030MR0638548
  6. Zhang, W., 10.5802/jtnb.179, J. Théor. Nombres Bordx. 8 (1996), 429-442. (1996) Zbl0871.11033MR1438480DOI10.5802/jtnb.179
  7. Toyoizumi, M., 10.4064/aa-55-3-229-232, Acta Arith. 55 (1990), 229-232. (1990) Zbl0702.11054MR1067970DOI10.4064/aa-55-3-229-232

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