A hybrid mean value involving two-term exponential sums and polynomial character sums

Di, Han. "A hybrid mean value involving two-term exponential sums and polynomial character sums." Czechoslovak Mathematical Journal 64.1 (2014): 53-62. <http://eudml.org/doc/261988>.

@article{Di2014,
abstract = {Let $q \ge 3$ be a positive integer. For any integers $m$ and $n$, the two-term exponential sum $C(m,n,k;q)$ is defined by $C(m,n,k;q) = \sum _\{a=1\}^q e (\{(ma^k +na)\}/\{q\})$, where $e(y)=\{\rm e\}^\{2\pi \{\rm i\} y\}$. In this paper, we use the properties of Gauss sums and the estimate for Dirichlet character of polynomials to study the mean value problem involving two-term exponential sums and Dirichlet character of polynomials, and give an interesting asymptotic formula for it.},
author = {Di, Han},
journal = {Czechoslovak Mathematical Journal},
keywords = {Dirichlet character of polynomials; two-term exponential sums; hybrid mean value; asymptotic formula; Dirichlet character of polynomials; two-term exponential sums; hybrid mean value; asymptotic formula},
language = {eng},
number = {1},
pages = {53-62},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A hybrid mean value involving two-term exponential sums and polynomial character sums},
url = {http://eudml.org/doc/261988},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Di, Han
TI - A hybrid mean value involving two-term exponential sums and polynomial character sums
JO - Czechoslovak Mathematical Journal
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 1
SP - 53
EP - 62
AB - Let $q \ge 3$ be a positive integer. For any integers $m$ and $n$, the two-term exponential sum $C(m,n,k;q)$ is defined by $C(m,n,k;q) = \sum _{a=1}^q e ({(ma^k +na)}/{q})$, where $e(y)={\rm e}^{2\pi {\rm i} y}$. In this paper, we use the properties of Gauss sums and the estimate for Dirichlet character of polynomials to study the mean value problem involving two-term exponential sums and Dirichlet character of polynomials, and give an interesting asymptotic formula for it.
LA - eng
KW - Dirichlet character of polynomials; two-term exponential sums; hybrid mean value; asymptotic formula; Dirichlet character of polynomials; two-term exponential sums; hybrid mean value; asymptotic formula
UR - http://eudml.org/doc/261988
ER -