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On the general Gauss sums and their fourth power mean

On the general Gauss sums and their fourth power mean
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Comments on "Tuberculosis infection control in MDR-TB designated hospitals in Jiangsu Province, China". [PDF]

J Clin Tuberc Other Mycobact Dis
Katkuri SN, Vadhithala V, Kumar A, Verma S, Dedeepya D.   +4 more
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Temporal fluctuation in lateral ventricle volume and its coupling with CSF inflow and global BOLD signal. [PDF]

Sci Rep
Cheng H, Kennedy DP.
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A new two-term exponential sums and its fourth power mean

Rendiconti del Circolo Matematico di Palermo Series 2, 2023
In the paper under review, the authors prove that for any odd prime \(p\), \[ C_4(p):=\sum_{m=0}^{p-1}\left|\sum_{n=0}^{p-1}\mathrm{e}\left(\frac{n^2(m+n)}{p}\right)\right|^4=2p^3+O(p^{5/2}), \] where \(\mathrm{e}(x)=e^{2\pi ix}\). They consider two cases when \(p-1\) is divisible by \(3\) or not.
Wang Xuexia, Wang Li
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Fourth power mean values of generalized Kloosterman sums

Functiones et Approximatio Commentarii Mathematici
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Li, Bag, Nilanjan
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On the fourth-power mean of the general cubic Gauss sums*

Lithuanian Mathematical Journal, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chang, Leran, Zhang, Wenpeng
semanticscholar   +4 more sources

On the fourth power mean of the generalized quadratic Gauss sums

Acta Mathematica Sinica, English Series, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Wen Peng, Lin, Xin
semanticscholar   +3 more sources

The Fourth Power Mean of the General 3-dimensional Kloostermann Sums mod p

Acta Mathematica Sinica, English Series, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Wen Peng, Lv, Xing Xing
semanticscholar   +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
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