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
[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