Results 261 to 270 of about 9,452,959 (273)

On the Fourth Power Mean of the Character Sums Over Short Intervals

Acta Mathematica Sinica, English Series, 2006
Let \(q \geq 5\) be an odd integer. The authors obtain an asymptotic formula for the mean value \(\sum^{**} | \sum_{1\leq a < q/8} \chi(a)| ^4\), where \(\sum^{**}\) denotes the summation over all primitive Dirichlet characters \(\chi\) modulo \(q\) with the property that \(\chi(-1)=-1\).
Wen Peng Zhang
exaly   +3 more sources

ON THE GENERAL k-TH KLOOSTERMAN SUMS AND ITS FOURTH POWER MEAN

Chinese Annals of Mathematics Series B, 2004
Let \(k\geq 1\) and let \(\chi\) be a character modulo \(q\). Define \[ S(m,n,k;\chi,q)= \sum^q_{a=1} \chi(a)\exp\Biggl({2\pi i\over q}(ma^k+ n\overline a^k)\Biggr), \] where \(a\overline a\equiv 1\pmod q\). In the case \(k=1\), \(\chi= \chi_0\), that is for the classical Kloosterman sum, \textit{H.
Wenpeng Zhang
exaly   +3 more sources

The fourth power mean of the general 2-dimensional Kloostermann sums mod p

Acta Mathematica Sinica, English Series, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Wen Peng, Li, Xiao Xue
semanticscholar   +4 more sources

A note on fourth power mean of the general two-term exponential sums

Mathematical Reports
Let $q$, $m$, $n$ be any integer with $q\ge 3$, and $\lambda$ a Dirichlet character $\bmod $ $q$. An explicit formula for the fourth power mean $$ \mathop{\sum}_{{m=1}\atop{(m,q)=1}}^{q} \biggl| \mathop{\sum}_{a=1}^{q} \lambda(a) e\biggl( \frac{ma^3+na}{q} \biggr) \biggr|^4 $$ is derived.
Mu, Yaya, Zhang, Tianping
openaire   +3 more sources

Fourth power mean values of generalized Kloosterman sums

Functiones Et Approximatio, Commentarii Mathematici
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nilanjan Bag
exaly   +2 more sources

The Mean Square of the Error Term for the Fourth Power Moment of the Zeta-Function

Proceedings of the London Mathematical Society, 1994
Let \[ \int^ T_ 0 \left | \zeta \Bigl( {1 \over 2} + it \Bigr) \right |^ 4dt = Tf (\log T) + E_ 2(T), \] where \(f\) is an appropriate quartic polynomial. It is shown here that \[ \int^ T_ 0 E_ 2(t)^ 2dt \ll T^ 2 (\log T)^ C \] for some constant \(C\). This remarkable result implies the estimates \(E_ 2 (T) \ll T^{2/3} (\log T)^ C\), and hence \(\zeta (
Ivić, Aleksandar, Motohashi, Yoichi
openaire   +2 more sources

On the hyper-Kloosterman sum and its fourth power mean

Studia Scientiarum Mathematicarum Hungarica, 2009
The main purpose of this paper is to study the calculating problem of the fourth power mean of the hyper-Kloosterman sums, and give an exact calculating formula for them.
openaire   +1 more source

Fourth Power Mean Value of Dirichlet’s L-Functions

1991
Let q≥ 2 be an integer. In this paper we shall consider the fourth power mean value of Dirichlet’s L-functions of the following type: Open image in new ...
openaire   +1 more source

On the fourth power mean of the generalized quadratic Gauss sums

, 2018
Wen-Peng Zhang, Xin Lin
semanticscholar   +1 more source

On the Fourth Power Mean of the Three-term Exponential Sums

, 2017
Hua-Ning Liu
semanticscholar   +1 more source