Results 61 to 70 of about 185 (158)
Gaussian distribution of short sums of trace functions over finite fields
, 2017 We show that under certain general conditions, short sums of ℓ-adic trace functions over finite fields follow a normal distribution asymptotically when the origin varies, generalising results of Erdős–Davenport, Mak–Zaharescu and Lamzouri. In particular,
CORENTIN PERRET–GENTIL +1 more
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A note on the Cochrane sum and its hybrid mean value formula
, 2003 In this paper, we use the properties of Gauss sums, primitive characters and the mean value theorems of Dirichlet L-functions to study the hybrid mean value of Cochrane sums and general Kloosterman sums, and give two sharp asymptotic ...
Zhang, Wenpeng, Liu, Huaning
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On the fourth power mean of the general Kloosterman sums
Journal of Number Theory, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the distribution in the arithmetic progressions of reducible quadratic polynomials
, 1995 By using Weil's estimate for Kloosterman sums, we obtain a result on the distribution of the sequence n(n+2), beyond the classical level, when a bilinear form with support over pairs of prime moduli is considered.
SALERNO, Saverio, VITOLO, Antonio
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On the fourth power mean of the analogous general Kloosterman sum
Journal of Number Theory, 2016 The authors study generalized Kloosterman sums \[ C(m,n,k,\chi;q)= \sum_{a=1}^{q}\chi(a)e\left(\frac{m\bar a^k+na}{q }\right), \] where \(q\), \(m\), \(n\), \(k\) are given positive integers, \(q \geq 3\), \(e(x)=e^{2\pi i x}\), \(a\bar a\equiv 1\pmod{q}\) and \(\chi\) is a character \(\mod{q}\).
Chen, Hui, Zhang, Tianping
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Bilinear forms with trace functions over arbitrary sets, and applications to Sato-Tate
, 2023 We prove non-trivial upper bounds for general bilinear forms with trace functions of bountiful sheaves, where the supports of two variables can be arbitrary subsets in $\mathbf{F}_p$ of suitable sizes.
Xi, Ping
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CoRR, 2009 In this paper, we construct two binary linear codes associated with multi-dimensional and $m -$multiple power Kloosterman sums (for any fixed $m$) over the finite field $\mathbb{F}_{q}$. Here $q$ is a power of two. The former codes are dual to a subcode of the binary hyper-Kloosterman code. Then we obtain two recursive formulas for the power moments of
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The arithmetic Kuznetsov formula on $GL(3)$, II: The general case
, 2019 We obtain the last of the standard Kuznetsov formulas for $SL(3,\Bbb{Z})$. In the previous paper, we were able to exploit the relationship between the positive-sign Bessel function and the Whittaker function to apply Wallach's Whittaker expansion; now we
Buttcane, Jack
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, 2006 Let χ be the Dirichlet character modulo q⩾3 and L(s,χ) denote the corresponding Dirichlet L-function. The mean value of |L′L(1,χ)|2k is studied and a few asymptotic formulae are given.
Zhang, Xiaobeng, Liu, Huaning
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On the mean value of a sum analogous to character sums over short intervals [PDF]
, 2008 summary:The main purpose of this paper is to study the mean value properties of a sum analogous to character sums over short intervals by using the mean value theorems for the Dirichlet L-functions, and to give some interesting asymptotic ...
Ganglian, Ren, Wenpeng, Zhang
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