Bounds for certain exponential sums

Author: tnny

August undefined, 2024

WebMar 26, 2024 · First, H. Hasse discovered a close connection between bounds for certain cubic exponential sums that generalize quadratic Gauss sums and the number of … Webbounds on certain types of exponential sums as well as being a tool for giving bounds on sum and product sets. We deﬁne the number of collinear triples, T(A,B), to be the …

Cherno bounds, and some applications 1 Preliminaries

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 ... WebNov 2, 2024 · Binomial exponential sums. We obtain new bounds of exponential sums modulo a prime with binomials . In particular, for , we improve the bound of Karatsuba … is cyclobenzaprine the same as diazepam

Exponential sums and polynomial congruences in two

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. Web1a. Exponential sums with multiplicative coe cients. Throughout f is a totally multiplicative function with jf(n)j 1 for all n. Diverse investigations in analytic number theory involve sums like S( ;N) := X n N f(n)e(n ) where e(t) = e2iˇt. Typically one wants non-trivial upper bounds on jS( ;N)j, which is WebLower 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 … rwam employee forms

Bounds for certain exponential sums Request PDF

Double Exponential Sums over Thin Sets - JSTOR

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 … 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 … is cyclobenzaprine safe while pregnantWebFeb 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 … rwam application form

"WebSep 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, … " - Bounds for certain exponential sums

Bounds for certain 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. …

Did you know?

WebMay 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,... WebThe two-term exponential sums originally arose in connection with Waring’s problem and the aim is to find optimal bounds. Many famous scholars such as H. Davenport (Darvenport and Heibronn, 1936), L.… Expand PDF View 2 excerpts, cites background Save Alert On …

WebJan 9, 2024 · Our main auxiliary result is an improved bound on certain related exponential sums over finite fields. ... The second one is around Igusa's conjecture for exponential sums with bounds in terms of ... Webtimes, and to satisfy certain bounds on its derivatives. Under suitable conditions, we can expect cancellations in the sum P n2I e(f(n)). The object of the theory of exponential sums is to detect such cancellations, i.e. to bound the said sum non-trivially. By the triangle inequality, the trivial bound is X n2I e(f(n)) ˝jIj;

WebDec 23, 2016 · Estimates are given for the exponential s u m ∑ x = 1 p exp (2 π i f (x) / p), p a prime and f a nonzero integer polynomial, of interest in cases where the Weil bound … 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....

WebNov 27, 2024 · Estimating exponential sums is a highlight in analytic number theory. This chapter investigates the main techniques to derive some non-trivial bounds for such sums, such as van der Corput’s methods, Weyl’s schift and Vinogradov’s process. More recent techniques, such as Vaughan’s identity, are treated in detail and non-trivial examples ...

WebNov 3, 2024 · There is not a commonly agreed definition on "without going through $\zeta(s)$," but it is possible to wrap up all the $\zeta$ processes between the exponential sum and the remainder of the PNT.. According to Titchmarsh's The theory of the Riemann zeta function, it is not difficult to convert growth condition of $\zeta(s)$ into a zero-free … rwam fax numberWebBOUNDS 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 this paper we consider exponential sums of the type (1.1) S(axn+ bx;pm) = X xmod pm e(axn+ bx=pm); and (1.2) S(axn+ bx;˜;pm) = X is cyclobenzaprine the same as valiumWebMar 1, 1999 · Bounds for Incomplete Hyper-Kloosterman Sums ... On certain exponential sums. J. Reine Angew. Math. (1933), pp. 158-176. ... On exponential sums. Sci. Record (New Series), 1 (1957), pp. 1-4. View in Scopus Google Scholar. 9. H.D. Kloosterman. On the representation of numbers in the formax 2 by 2 cz 2 dt 2. is cyclobenzaprine the same as meloxicamWebear forms of Kloosterman and Gauss sums in this setting, based on new bounds on the number of solutions to certain modular congruences in F q[T] . Contents 1. Introduction 2 2. Notation 3 2.1. General notation 3 2.2. Modular congruences 4 2.3. Exponential function in function ﬁelds 5 3. Main results 6 3.1. Bilinear forms with Kloosterman sums ... rwam customer serviceWebJun 28, 2024 · While establishing the conjecture of Erdös on 2n \atopwithdelims ()n, Granville and Ramaré converted this problem into one dealing with certain exponential sums. More precisely, one needs to estimate an upper bound of the sums of the form: \begin {aligned} S:=\sum _ {y< y'} \Lambda (n) e (x/n). \end {aligned} rwam termination formWebOct 31, 2000 · or, more simply, multiplying the two bounds and taking the square root we obtain the somewhat weaker result max I Sa (X, Y) I< I X12/31 yl2/3tl/2pl/8K ... R. Canetti, J. B. Friedlander and I. E. Shparlinski, 'On certain exponential sums and the distribution of Diffie-Hellman triples', J. London Math. Soc., 59 (1999), 799-812. MR 2000g: 1 1079 ... rwam medical evidence formWebBOUNDS 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 … rwam health insurance