Pure and mixed exponential sums

Author: gidx

August undefined, 2024

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)); … 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.

Mean value of mixed exponential SUMS - ResearchGate

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 … WebWe obtain upper bounds for mixed exponential sums of the type S (\chi ,f,p^m ) = \sum\nolimits_ {x = 1}^ {p^n } {\chi (x)e} _ {p^m } (ax^n + bx) where p m is a prime power with m⩾ 2 and X is a multiplicative character (mod p m ). If X is primitive or p⫮ (a, b) then we obtain S (χ, f, p m ) ⩽2 np 2/3 m. If X is of conductor p and p⫮ ... ukulele chords for amazing grace

AN IMPROVED MORDELL TYPE BOUND FOR EXPONENTIAL SUMS

WebMar 6, 2002 · A uniform version of the Schanuel conjecture is discussed that has some model-theoretical motivation. This conjecture is assumed, and it is proved that any ‘non-obviously-contradictory’ system of equations in the form of exponential sums with real exponents has a solution. WebJ. H. H. Chalk, “On Hua’s estimate for exponential sums,” Mathematika, 14, 115–123 (1987). Article MathSciNet Google Scholar T. Cochrane and Z. Zheng, “Pure and mixed … 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 ... ukulele chords f

Pure and mixed exponential sums

WebMar 1, 2015 · 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 …

Did you know?

WebPURE AND MIXED EXPONENTIAL SUMS ERRATA TODD COCHRANE AND ZHIYONG ZHENG Theorem 1.1 (iii) needs a small adjustment in the case where p= 3 and m t= 3, as noted by … WebPublished 1999. Mathematics. Acta Arithmetica. We 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 m is a prime power with m ≥ 2, χ is a …

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 (x)ep m (f(x)), where p m is a prime power ...

WebThe goals of this paper are threefold; first, to point out the similarity between exponential sums over finite fields and exponential sums over residue class rings (mod p) with m ≥ 2; … 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.

WebWe obtain upper bounds for mixed exponential sums of the type S (\chi ,f,p^m ) = \sum\nolimits_ {x = 1}^ {p^n } {\chi (x)e} _ {p^m } (ax^n + bx) where p m is a prime power …

WebJ. H. H. Chalk, “On Hua’s estimate for exponential sums,” Mathematika, 14, 115–123 (1987). Article MathSciNet Google Scholar T. Cochrane and Z. Zheng, “Pure and mixed exponential sums,” Acta Arith., 91, 249–278 (1999). MATH MathSciNet Google Scholar ukulele chords fly me to the moonWebWe 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 … ukulele chords children songshttp://yadda.icm.edu.pl/yadda/element/bwmeta1.element.bwnjournal-article-aav91i3p249bwm ukulele chords for broadway songsWebThe 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 … ukulele chords ed sheeranWebexponential 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 … thompson milk thistle 42000WebFeb 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 ... ukulele chords for gentle on my mindWebAn 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. ukulele chords for god bless america