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ON THE GENERAL k-TH KLOOSTERMAN SUMS AND ITS FOURTH POWER MEAN
Chinese Annals of Mathematics, 2004Let \(k\geq 1\) 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.
Liu, Hongyan, Zhang, Wenpeng
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On the fourth-power mean of the general cubic Gauss sums*
Lithuanian Mathematical Journal, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chang, Leran, Zhang, Wenpeng
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On the Fourth Power Mean of the Character Sums Over Short Intervals
Acta Mathematica Sinica, English Series, 2006Let \(q \geq 5\) 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 \(\chi(-1)=-1\).
Zhang, Wenpeng, Wang, Xiaoying
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On the fourth power mean of the generalized quadratic Gauss sums
Acta Mathematica Sinica, English Series, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Wen Peng, Lin, Xin
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An improved estimate of the fourth power mean of the general $3$-dimensional Kloosterman sum mod $p$
Functiones et Approximatio Commentarii Mathematici, 2021Recently, Zhang and Lv find an asymptotic formula for the fourth power mean of the general $3$-dimensional Kloosterman sum mod $p$. In this article we prove an improvement of their asymptotic formula.
Nilanjan Bag, Rupam Barman
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The Fourth Power Mean of the General 3-dimensional Kloostermann Sums mod p
Acta Mathematica Sinica, English Series, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Wen Peng, Lv, Xing Xing
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The fourth power mean of the general 2-dimensional Kloostermann sums mod p
Acta Mathematica Sinica, English Series, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Wen Peng, Li, Xiao Xue
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Fourth power mean of the general 4-dimensional Kloosterman sum mod p
Research in Number Theory, 2020In this article, we prove an asymptotic formula for the fourth power mean of a general 4-dimensional Kloosterman sum. We use a result of P. Deligne, which counts the number of $$\mathbb {F}_p$$ -points on the surface $$\begin{aligned} (x-1)(y-1)(z-1)(1-xyz)-uxyz=0, ~ u\ne 0, \end{aligned}$$ and then take an average of the error terms over u to ...
Nilanjan Bag, Rupam Barman
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On the hyper-Kloosterman sum and its fourth power mean
Studia Scientiarum Mathematicarum Hungarica, 2009The 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.
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