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Degrees of generalized Kloosterman sums

Forum Mathematicum
Abstract The modern study of the exponential sums is mainly about their analytic estimates as complex numbers, which is local. In this paper, we study one global property of the exponential sums by viewing them as algebraic integers. For a kind of generalized Kloosterman sums, we present their degrees as algebraic integers.
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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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On some hybrid power moments of products of generalized quadratic Gauss sums and Kloosterman sums*

Lithuanian Mathematical Journal, 2018
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Göran Djanković, Nikola Lelas
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Generalized Kloosterman sum with primes

Proceedings of the Steklov Institute of Mathematics, 2017
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Newton polygons of L-functions for two-variable generalized Kloosterman sums

International Journal of Number Theory, 2023
In this paper, we study the Newton polygon of the [Formula: see text]-function of a generalized Kloosterman polynomial with two variables over finite fields. We give the explicit form of the monomial basis of the top dimensional cohomology space of the [Formula: see text]-adic complex associated to the [Formula: see text]-function.
Wang, Chunlin, Yang, Liping
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Summation formulas for general Kloosterman sums

Journal of Soviet Mathematics, 1982
N. V. Kuznetsov's summation formula is generalized to the case of a discrete subgroup G⊂SL2(ℝ) and a system of multiplicators χ, satisfying certain not too restrictive conditions. In the arithmetic cases, when G is a congruence-subgroup in SL2(ℤ), these conditions are satisfied. N. V. Kuznetsov's formula has been proved for the case G=SL2(ℤ)., χ=1.
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A new hybrid power mean involving the generalized quadratic Gauss sums and sums analogous to Kloosterman sums *

Lithuanian Mathematical Journal, 2017
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Xingxing Lv, Wenpeng Zhang
exaly   +3 more sources

Symmetric power 𝐿-functions for families of generalized Kloosterman sums

Transactions of the American Mathematical Society, 2016
We construct relative p p -adic cohomology for a family of toric exponential sums fibered over the torus.
Haessig, C. Douglas, Sperber, Steven
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Bounds on bilinear sums of generalized Kloosterman sums over arbitrary sets

Journal of Number Theory
Tianping Zhang
exaly   +2 more sources

On a Problem of D. H. Lehmer and General Kloosterman Sums

Acta Mathematica Sinica, English Series, 2004
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