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Bounds for certain exponential sums

WebNov 2, 2024 · Binomial exponential sums Igor E. Shparlinski, Jose Felipe Voloch We obtain new bounds of exponential sums modulo a prime with binomials . In particular, for , we improve the bound of Karatsuba (1967) from to for any , and then use it to improve the bound of Akulinichev (1965) from to for . WebJan 11, 2024 · We use analytic methods to obtain an explicit formula for the fourth power mean. ∑ χ mod q ∑ ′ m = 1 q ∑ ′ a = 1 q χ ( a) e m a k + n a q 4, where e ( y) = e 2 π i y, χ is a Dirichlet character modulo q and ∑ ′ a = 1 q denotes the summation over all a such that ( a, q) = 1. This extends the result of Chen, Ai and Cai by ...

BOUNDS FOR CERTAIN EXPONENTIAL SUMS Todd Cochrane …

WebJul 3, 2024 · We use an estimate of Aksoy Yazici, Murphy, Rudnev and Shkredov (2016) on the number of solutions of certain equations involving products and differences of sets in … Webimproved, which leads to a sharper bound in certain ranges. The proofs both build on the recently proved main conjecture for Vino-gradov’s mean value theorem. We present two selected applications: First, we prove a new k-th derivative test for the number of integer points close to a curve by an exponential sum approach. This yields a stronger ... rj horner chest of drawers https://soldbyustat.com

[1811.00765] Binomial exponential sums - arXiv.org

WebDec 1, 2024 · In the streamlined derivation at the end of Section 1 of Property (5) for sub-exponential zero-mean r.v.’s X, we used the bound on exponential moments of the r.v. X given by Property (4) to first bound the absolute moments of X as in (4), and then we used the Maclaurin series for the exponential function to bound exponential moments of X, … WebFeb 1, 2024 · Friedlander and Iwaniec [7] have used these sums to derive new results on the divisor function in arithmetic progressions; • Heath-Brown [8] has estimated such … 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. rj holmes swindon

arXiv:1408.5794v2 [math.NT] 22 Feb 2016

Category:[math/0612765] Bounds on certain Higher-Dimensional …

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Bounds for certain exponential sums

upper bound of exponential function - Mathematics Stack Exchange

Webstart with the statement of the bound for the simple case of a sum of independent Bernoulli trials, i.e. the case in which each random variable only takes the values 0 or 1. For example, this corresponds to the case of tossing unfair coins, each with its own probability of heads, and counting the total number of heads. Theorem 4 (Cherno Bounds). WebNew exponential sum bounds are presented in §3. They are based on combining Corollary 3 with known estimates on the parameter B from the second spacing problem (see the Acknowledgement below). The conclusion is stated as Theorem 4. In §4, we establish our new estimate on ζ(1 2+it) . Theorem 5. ζ 1 2 +it ≪ t 1384+ε.

Bounds for certain exponential sums

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WebJun 16, 2015 · What are the best bounds currently known for the following exponential sum: ∑ x < p ≤ 2 x e ( α p k) for values of α far from a rational with small denominator. ( p …

WebFeb 13, 2012 · We establish new bounds for the density of integer solutions to the equation $f=0$, using an iterated version of Heath-Browns $q$-analogue of van der Corput's method of exponential sums.... WebDec 26, 2006 · We describe a new method to bound certain higher-dimensional exponential sums which are associated with tori in symplectic groups over finite fields. …

WebJan 1, 2000 · Bounds for certain exponential sums January 2000 Authors: Todd Cochrane Kansas State University Zhiyong Zheng No full-text available Citations (22) ... WebDec 1, 2024 · Here we provide some new bounds on quadrinomial exponential sums using the techniques in [13]. We thus define (1.1) Ψ ( X) = a X k + b X ℓ + c X m + d X n. …

Webtry each method in parallel until one succeeds. "ParallelBestQuality". try each method in parallel and return the best result. "IteratedSummation". use iterated univariate summation. Automatic. automatically selected method. "HypergeometricTermFinite". special finite hypergeometric term summation.

WebBounds on the radius of convergence can be computed using the asymptotics of a k. One that works for all s is a k k! << ( k ( s + 1)) k − 1 k k + 1 / 2 e − k so it converges for r < 1 ( ( + 1)). This can be … smpp chariteWebBOUNDS FOR CERTAIN EXPONENTIAL SUMS Todd Cochrane and Zhiyong Zheng1 To the memory of professor L. K. Hua on the occasion of his 90th birthday 1. Introduction In … smp parts mod 1.7.10Webone may arrive at exponential sum bounds that depend on knowledge of various derivatives. These methods, for instance, have been very sucessuly applied to the Riemann zeta function. 2. Complete sums Complete sums typically refer to exponential sums over finite fields. In what follows we denote by F = F q a field of prime power order. smpp command outbindWebApr 20, 2024 · Lower bound on exponential sums Asked 2 years, 11 months ago Modified 2 years, 4 months ago Viewed 660 times 8 Let k ≥ 2. Consider the following norm of … smp payment scheduleWebSep 1, 2024 · In the past few decades, there have been extensive study and application of the exponential sum S_k (\vec {a}). For instance, using Deligne’s theorem on weights, … rj home repairWebMay 1, 2005 · Exponential sums have been used to estimate correlation in several previous papers starting with the results of Cai, Green and Thierauf [CGT] for symmetric polynomials and also in [Gr99,Gr02,... rj hollowayWebLower bound on certain exponential sums and expressions related to them Asked 8 years, 11 months ago Modified 8 years, 11 months ago Viewed 241 times 3 Let G ( α, x) = ∑ n … r j horner furniture ebay