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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 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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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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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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The Mean Square of the Error Term for the Fourth Power Moment of the Zeta-Function
Proceedings of the London Mathematical Society, 1994Let \[ \int^ T_ 0 \left | \zeta \Bigl( {1 \over 2} + it \Bigr) \right |^ 4dt = Tf (\log T) + E_ 2(T), \] 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
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A new two-term exponential sums and its fourth power mean
Rendiconti del Circolo Matematico di Palermo Series 2, 2023Xuexia Wang, Wang Li
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Cervical cancer prevention and control in women living with human immunodeficiency virus
Ca-A Cancer Journal for Clinicians, 2021Philip E Castle, Vikrant V Sahasrabuddhe
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