On the -th power mean of with the weight of Gauss sums
Czechoslovak Mathematical Journal (2009)
- Volume: 59, Issue: 3, page 781-789
- ISSN: 0011-4642
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topRen, Dongmei, and Yi, Yuan. "On the $2k$-th power mean of $\frac{L^{\prime }}{L}(1,\chi )$ with the weight of Gauss sums." Czechoslovak Mathematical Journal 59.3 (2009): 781-789. <http://eudml.org/doc/37958>.
@article{Ren2009,
abstract = {The main purpose of this paper is to study the hybrid mean value of $\frac\{L^\{\prime \}\}\{L\}(1,\chi )$ and Gauss sums by using the estimates for trigonometric sums as well as the analytic method. An asymptotic formula for the hybrid mean value $\sum _\{\chi \ne \chi _0\} |\tau (\chi )| |\frac\{L^\{\prime \}\}\{L\}(1,\chi )|^\{2k\}$ of $\frac\{L^\{\prime \}\}\{L\}$ and Gauss sums will be proved using analytic methods and estimates for trigonometric sums.},
author = {Ren, Dongmei, Yi, Yuan},
journal = {Czechoslovak Mathematical Journal},
keywords = {Dirichlet L-function; Gauss sums; asymptotic formula; Dirichlet L-function; Gauss sum; asymptotic formula},
language = {eng},
number = {3},
pages = {781-789},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the $2k$-th power mean of $\frac\{L^\{\prime \}\}\{L\}(1,\chi )$ with the weight of Gauss sums},
url = {http://eudml.org/doc/37958},
volume = {59},
year = {2009},
}
TY - JOUR
AU - Ren, Dongmei
AU - Yi, Yuan
TI - On the $2k$-th power mean of $\frac{L^{\prime }}{L}(1,\chi )$ with the weight of Gauss sums
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 3
SP - 781
EP - 789
AB - The main purpose of this paper is to study the hybrid mean value of $\frac{L^{\prime }}{L}(1,\chi )$ and Gauss sums by using the estimates for trigonometric sums as well as the analytic method. An asymptotic formula for the hybrid mean value $\sum _{\chi \ne \chi _0} |\tau (\chi )| |\frac{L^{\prime }}{L}(1,\chi )|^{2k}$ of $\frac{L^{\prime }}{L}$ and Gauss sums will be proved using analytic methods and estimates for trigonometric sums.
LA - eng
KW - Dirichlet L-function; Gauss sums; asymptotic formula; Dirichlet L-function; Gauss sum; asymptotic formula
UR - http://eudml.org/doc/37958
ER -
References
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