Results 91 to 100 of about 31,766 (124)

Uniform bounds for Kloosterman sums of half-integral weight with applications

Forum mathematicum, 2023
Sums of Kloosterman sums have deep connections with the theory of modular forms, and their estimation has many important consequences. Kuznetsov used his famous trace formula and got a power-saving estimate with respect to x with implied constants ...
Qihang Sun
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On the General Kloosterman Sums

Journal of Mathematical Sciences, 2005
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A generalization of power moments of Kloosterman sums

Archiv der Mathematik, 2007
We find an expression for a sum which can be viewed as a generalization of power moments of Kloosterman sums studied by Kloosterman and Salie.
Hi-Joon Chae, Dae San Kim
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Mean Value of Generalized Bernoulli Numbers, General Kloosterman Sums and Character Sums

, 2013
Zhang Xiaobeng, L. Huaning
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On a generalization of Kloosterman sums

Mathematical Notes, 2015
For integers \(u, v, w\) and natural numbers \(q\), \(d\) with \(d\mid q\). We define \[ K_{q,d}\left(u, v; w\right)=\mathop{\mathop{\sum_{z=1}^{q}}_{(z,q)=1}}_{z\equiv w \;(\bmod d)} e\left(\frac{uz+vz^{-1}}{q}\right), \] where \(e(x)=\text{e}^{2\pi ix}\).
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Some novel identities for analogues of Dedekind sums, Hurwitz zeta-function and general Kloosterman sum

Acta Mathematica Hungarica, 2022
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The generating fields of twisted Kloosterman sums

International Journal of Number Theory
We use the Kloosterman sheaves constructed by Fisher to show when two twisted Kloosterman sums differ by a factor of a [Formula: see text]th root of unity, and use p-adic analysis to prove the non-vanishing of twisted Kloosterman sums. Then, we determine generating fields of twisted Kloosterman sums by these results.
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ON THE GENERAL k-TH KLOOSTERMAN SUMS AND ITS FOURTH POWER MEAN

Chinese Annals of Mathematics, 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.
Liu, Hongyan, Zhang, Wenpeng
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On a Problem of D. H. Lehmer and General Kloosterman Sums

Acta Mathematica Sinica, English Series, 2004
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General Kloosterman sums over ring of Gaussian integers

2020
?????????????????????? ???????? ?????????????????????? K(m,n;k;q) ?????? Z ?????????????? S. Kanemitsu, Y. Tanigawa, Yi. Yuan, Zhang Wenpeng ?? ???? ?????????????????????? ???????????????? D. H. Lehmer. ?? ?????? ???????????? ???????????????? ?????????????? ???????????? K(??,??;k;??) ?????? Z[i]. ?????????? ???????????????????? ???????? K??(??,??;h,q;k)
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