Pure and mixed exponential sums
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 … 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)); … WebFeb 27, 2014 · 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 ...
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 ... WebPure and mixed exponential sums. ... On exponential sums in finite fields, Amer. J. Math. 88 (1966), 71-105. [2] J. H. H. Chalk, On Hua's estimate for exponential sums, Mathematika 34 (1987), 115-123. [3] J. R. Chen, On Professor Hua's estimate of exponential sums, Sci. Sinica 20 (1977), 711-719.
WebNov 8, 2013 · Cochrane T, Zheng ZY: Pure and mixed exponential sums. Acta Arith. 1999, 91: 249–278. MathSciNet Google Scholar Cochrane T, Pinner C: A further refinement of Mordell’s bound on exponential sums. Acta Arith. 2005, 116: 35–41. 10.4064/aa116-1-4. Article MathSciNet Google Scholar WebPure and mixed exponential sums Todd Cochrane; Zhiyong Zheng. Acta Arithmetica (1999) Volume: 91, Issue: 3, page 249-278; ISSN: 0065-1036; Access Full Article top Access to …
WebMar 19, 2014 · Cochrane T, Zheng Z: Pure and mixed exponential sums. Acta Arith. 1999, 91: 249–278. MathSciNet MATH Google Scholar ... Cochrane T, Pinner C: Using Stepanov’s method for exponential sums involving rational functions. J. Number Theory 2006, 116: 270–292. 10.1016/j.jnt.2005.04.001.
Webexponential sums to mixed exponential sums. When all of the critical points are of multiplicity one then we obtain an explicit formula for the exponential sum, generalizing … bridge street car park shrewsburyWebIn this paper we give a survey of recent work by the authors and others on pure and mixed exponential sums of the type can vanilla beans be grown at homecan vanilla gift cards be reloadedWebthe 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 … can vanilla cards be used onlineWebAlthough Mordell only considered pure exponential sums his method easily extends to the case of mixed sums. Davenport [5] obtained some re nements of Mordell’s work but his results were superseded by Weil; see also Shparlinski [11, p.88]. For further discussion of the case of monomials see [6] and [8], and for binomials [7], [1], [3] and [14]. bridge street carpets buckinghamWebAn 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 solution of various problems in number theory; in this article we will just play around with a few examples, draw their graphs and try to explain some of their features. can vanilla extract be added to coffeeWebApr 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. can vanilla beans be grown in the us