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 … 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 …
Pure and mixed exponential sums
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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 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⫮ ...
WebAn 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 … WebAn 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.
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. 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 ...
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
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 … shrewsbury to baschurch bus timetableWebThe 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 … shrewsbury to crewe railway lineWebWe 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 … shrewsbury things to do with kidsWebPure 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 full text Full (PDF) How to cite top. MLA; BibTeX; RIS; … shrewsbury to bomere heathWebThe 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 … shrewsbury to barmouth trainWebPURE 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 … shrewsbury to bayston hillhttp://matwbn.icm.edu.pl/ksiazki/aa/aa91/aa9136.pdf shrewsbury to aberystwyth