Pure and mixed exponential sums
WebMay 3, 2024 · We establish bounds for triple exponential sums with mixed exponential and linear terms. The method we use is by Shparlinski [‘Bilinear forms with Kloosterman and Gauss sums’, Preprint, 2016, arXiv:1608.06160] together with a bound for the additive energy from Roche-Newton et al. WebWe obtain explicit formulae and sharp estimates for pure and mixed exponential sums of the type S(f, pm) = ∑pm x=1 epm (f(x)) and S(χ, f, pm) = ∑pm x=1 χ(x)epm (f(x)), where p …
Pure and mixed exponential sums
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WebJan 1, 2002 · In this paper we give a survey of recent work by the authors and others on pure and mixed exponential sums of the type p m X x=1 epm(f(x)); p m X x=1 (g(x))epm(f(x)); … WebAug 1, 2006 · We obtain explicit formulae and sharp estimates for pure and mixed exponential sums of the type S(f;pm) = Pp m x=1ep m (f(x)) and S(;f;p m) = Pp m x=1 (x)ep m (f(x)), where p m is a prime power ...
Webthe sum S(χ,f,pm). The proof of Theorem 1.1 is given in Sections 6 and 7, and the case p= 2 is dealt with in Section 8. Our strategy for estimating the mixed exponential sum Sα is to … WebAug 13, 2014 · For any integers m and n, the two-term exponential sum C ( m, n, k; q) is defined by C (m,n,k;q) = \sum\limits_ {a = 1}^q {e ( (ma^k + na)/q)} , where e (y) = e^ {2\pi iy} . In this paper, we use the properties of Gauss sums and the estimate for Dirichlet character of polynomials to study the mean value problem involving two-term exponential ...
WebApr 1, 2007 · We obtain explicit formulae and sharp estimates for pure and mixed exponential sums of the type S(f;pm) = Pp m x=1ep m (f(x)) and S(;f;p m) = Pp m x=1 … WebApr 10, 2024 · A. Weil, “On some exponential sums,” Proceedings of the National Academy of Sciences of the United States of America, vol. 34, pp. 203–210, 1948. View at: Publisher Site Google Scholar W. P. Zhang, “Moments of generalized quadratic Gauss sums weighted by L-functions,” Journal of Number Theory , vol. 92, pp. 304–314, 2002.
WebThe result obtained here generalizes the upper bound for pure exponential sums obtained in [5], which was a sharpening of earlier bounds of Chalk [2],Ding [7], [8], Loh [21] and …
Webexponential sums on an affine variety defined over Fq. While this is the natural order of the work, what we do, in fact, ... n X Fq, W,1(f)) is pure of weight n (it is always mixed of weights < n by [10]). In the case of mixed weights, we can in certain cases calculate the number of eigenvalues of a given weight. We plan to return to this topic ... borg infestationhave a great thursday everyoneWebAug 10, 2024 · This is an expository paper on algebraic aspects of exponential sums over finite fields. This is a new direction. Various examples, results and open problems are … have a great thursday memeshttp://yadda.icm.edu.pl/yadda/element/bwmeta1.element.bwnjournal-article-aav91i3p249bwm have a great thanksgiving weekWebWe obtain explicit formulae and sharp estimates for pure and mixed exponential sums of the type S(f;pm) = Pp m x=1ep m (f(x)) and S(;f;p m) = Pp m x=1 (x)ep m (f(x)), where p m … have a great thursday messageWebAn exponential sum is an expression of the form \[ \sum_{n=1}^N e^{2 \pi i f(n)},\] where \( f \) is a real-valued function defined on the positive integers. Such sums are used in the … have a great time doing sth什么意思WebThe above identity reduces the mixed exponential sum to a study of pure exponential sums of the type p S(f,p ~) := ~--~ef(f(x)), (1.11) where f is a polynomial with integer coefficients. These sums have been studied extensively Is] l) The … have a great time camping vacation images