Results 11 to 20 of about 359 (42)
Improving estimates for discrete polynomial averages [PDF]
, 2020 For a polynomial $P$ mapping the integers into the integers, define an averaging operator $A_{N} f(x):=\frac{1}{N}\sum_{k=1}^N f(x+P(k))$ acting on functions on the integers.
Han, Rui +4 more
core +3 more sources
Mean value estimates for odd cubic Weyl sums [PDF]
, 2014 We establish an essentially optimal estimate for the ninth moment of the exponential sum having argument $\alpha x^3+\beta x$. The first substantial advance in this topic for over 60 years, this leads to improvements in Heath-Brown's variant of Weyl's ...
Wooley, Trevor D.
core +4 more sources
INVERSIVE CONGRUENTIAL GENERATOR WITH A VARIABLE SHIFT OF PSEUDORANDOM POINTS OVER THE COMPLEX PLANE
, 2015 Consider the generator of pseudorandom points on unit square produced by the inversive congruential recursion over the ring of Gaussian integers. Study the exponential sums on sequences of these points.
T. T. Vinh
semanticscholar +1 more source
One kind sixth power mean of the three-term exponential sums
Open Mathematics, 2017 In this paper, we use the estimate for trigonometric sums and the properties of the congruence equations to study the computational problem of one kind sixth power mean of the three-term exponential sums.
Wang Xiaoying, Li Xiaoxue
doaj +1 more source
Cancellations Amongst Kloosterman Sums
, 2016 We obtain several estimates for bilinear form with Kloosterman sums. Such results can be interpreted as a measure of cancellations amongst with parameters from short intervals.
Shparlinski, I. E., Zhang, T. P.
core +1 more source
On Primes Represented by Quadratic Polynomials
, 2007 This is a survey article on the Hardy-Littlewood conjecture about primes in quadratic progressions. We recount the history and quote some results approximating this hitherto unresolved conjecture.Comment: six(6) pages, minor changes were ...
Baier, Stephan, Zhao, Liangyi
core +5 more sources
Multiple Exponential and Character Sums with Monomials
, 2013 We obtain new bounds of multivariate exponential sums with monomials, when the variables run over rather short intervals. Furthermore, we use the same method to derive estimates on similar sums with multiplicative characters to which previously known ...
Shparlinski, Igor
core +1 more source
Almost all palindromes are composite
, 2004 We study the distribution of palindromic numbers (with respect to a fixed base $g\ge 2$) over certain congruence classes, and we derive a nontrivial upper bound for the number of prime palindromes $n\le x$ as $x\to\infty$.
Banks, William D. +2 more
core +2 more sources
Note on sums involving the Euler function
, 2018 In this note, we provide refined estimates of the following sums involving the Euler totient function: $$\sum_{n\le x} \phi\left(\left[\frac{x}{n}\right]\right) \qquad \text{and} \qquad \sum_{n\le x} \frac{\phi([x/n])}{[x/n]}$$ where $[x]$ denotes the ...
Chern, Shane
core +1 more source
Abel Summation of Ramanujan-Fourier Series [PDF]
, 2015 Using Abel summation the paper proves a weak form of the Wiener-Khinchin formula for arithmetic functions with point-wise convergent Ramanujan-Fourier expansions.
Washburn, John
core