Results 21 to 30 of about 185 (158)
On the Generalization of Lehmer Problem and High-Dimension Kloosterman Sums [PDF]
The Scientific World Journal, 2014 For any fixed integerk≥2and integerrwithr, p=1, it is clear that there existkintegers1≤ai≤p-1 i=1, 2, …, ksuch thata1a2⋯ak≡r mod p. LetN(k,r;p)denote the number of alla1, a2, ⋯aksuch thata1a2⋯ak≡r mod pand 2†a1+a2+⋯ + ak. In this paper, we will use the analytic method and the estimate for high-dimension Kloosterman sums to study the asymptotic ...
Guohui Chen, Han Zhang
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Stratification and averaging for exponential sums: bilinear forms with generalized Kloosterman sums [PDF]
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2020 We prove non-trivial bounds for bilinear forms with hyper-Kloosterman sums with characters modulo a prime $q$ which, for both variables of length $M$, are non-trivial as soon as $M\geq q^{3/8+δ}$ for any $δ>0$. This range, which matches Burgess's range, is identical with the best results previously known only for simpler exponentials of monomials ...
Kowalski, Emmanuel +2 more
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New identities involving Hardy sums $S_3(h,k)$ and general Kloosterman sums
AIMS Mathematics, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wenjia Guo, Yuankui Ma, Tianping Zhang
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Asymptotic distribution of Kloosterman sums
, 2022 Tese de Mestrado, Matemática, 2022, Universidade de Lisboa, Faculdade de CiênciasIn this thesis, we will study Kloosterman sums which are a particular case of exponential sums. Our goal is to obtain the best possible bound for these sums.
Dias, Carlos Manuel Martins
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Distribution of short sums of classical Kloosterman sums of prime powers moduli [PDF]
, 2019 Corentin Perret-Gentil proved, under some very general conditions, that short sums of $\ell$-adic trace functions over finite fields of varying center converges in law to a Gaussian random variable or vector.
RICOTTA, Guillaume, Guillaume Ricotta
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Visual properties of generalized Kloosterman sums
Journal of Number Theory, 2016 For a positive integer $m$ and a subgroup $Λ$ of the unit group $(\mathbb{Z}/m\mathbb{Z})^\times$, the corresponding generalized Kloosterman sum is the function $K(a,b,m,Λ) = \sum_{u \in Λ}e(\frac{au + bu^{-1}}{m})$. Unlike classical Kloosterman sums, which are real valued, generalized Kloosterman sums display a surprising array of visual features when
Burkhardt, Paula +5 more
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Generalized Twisted Kloosterman Sum Over ℤ[i] [PDF]
Ukrainian Mathematical Journal, 2014 The twisted Kloosterman sums over Z were studied by V. Bykovsky, A.Vinogradov, N. Kuznetsov, R. W. Bruggeman, R. J. Miatello, I. Pacharoni, A. Knightly, and C. Li. In our paper, we obtain similar estimates for K χ (α, β; γ; q) over ℤ[i] and improve the estimates obtained for the sums of this kind with ...
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Families of generalized Kloosterman sums
, 2013 36 pages, 4 ...
Haessig, C. Douglas, Sperber, Steven
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Kuznetsov Formulas for Generalized Kloosterman Sums
Rocky Mountain Journal of Mathematics, 1997 The Kuznetsov trace formula [\textit{N. V. Kuznetsov}, Mat. Sb., Nov. Ser. 111(153), 334-383 (1980; Zbl 0427.10016)] relates a weighted sum of classical Kloosterman sums to a weighted sum of Fourier coefficients of \(GL(2)\) automorphic forms and other spectral information.
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Kloosterman sums in residue classes
, 2015 We prove upper bounds for sums of Kloosterman sums against general arithmetic weight functions. In particular, we obtain power cancellation in sums of Kloosterman sums over arithmetic progressions, which is of square-root strength in any xed primitive ...
Milicevic, D. +3 more
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