Zobrazeno 1 - 10
of 16
pro vyhledávání: '"George Shakan"'
Autor:
George Shakan, Andrew Granville
Publikováno v:
Acta Mathematica Hungarica. 161:700-718
Let A be a finite subset of $$\mathbb{Z}^n$$ , which generates $$\mathbb{Z}^n$$ additively. We provide a precise description of the N-fold sumsets NA for N sufficiently large, with some explicit bounds on “sufficiently large.”
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c9f31fcb8b79f9885c587e939b22f80c
https://doi.org/10.1007/s10474-020-01073-y
https://doi.org/10.1007/s10474-020-01073-y
Publikováno v:
Analysis at Large ISBN: 9783031053306
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f7a980a421f604e30f4d87fb3762432b
https://doi.org/10.1007/978-3-031-05331-3_6
https://doi.org/10.1007/978-3-031-05331-3_6
Publikováno v:
Journal of Mathematical Analysis and Applications. 518:126784
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d5d664c55c583a421796f4197dd03358
https://doi.org/10.1016/j.jmaa.2022.126784
https://doi.org/10.1016/j.jmaa.2022.126784
Publikováno v:
Springer Proceedings in Mathematics & Statistics ISBN: 9783030679958
We show that if \(A=\{a_1< a_2< \ldots < a_k\}\) is a set of real numbers such that the differences of the consecutive elements are distinct, then for and finite \(B \subset \mathbb {R}\), $$ |A+B|\gg |A|^{1/2}|B|. $$ The bound is tight up to the con
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ed00aae1292838d0c15f13bf78cd2715
https://doi.org/10.1007/978-3-030-67996-5_24
https://doi.org/10.1007/978-3-030-67996-5_24
Autor:
Robert J. Lemke Oliver, Ayla Gafni, David Lowry-Duda, George Shakan, Theresa C. Anderson, Ruixiang Zhang
We study two polynomial counting questions in arithmetic statistics via a combination of Fourier analytic and arithmetic methods. First, we obtain new quantitative forms of Hilbert's Irreducibility Theorem for degree $n$ polynomials $f$ with $\mathrm
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6cd702676cb3c80d265c2500b6f6dd1f
Autor:
George Shakan
Let $A \subset \mathbb{F}_p$ with $|A| > 1$. We show there is a $d \in \mathbb{F}_p^{\times}$ such that $d \cdot A$ contains a gap of size at least $2p/ |A| - 2 $.
3 pages
3 pages
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ad99ddef209ae2a857143d1fd4767c8b
Publikováno v:
Mathematische Annalen
We obtain asymptotics for sums of the form $$\begin{aligned} \sum _{n=1}^P e\left( {\alpha }_k\,n^k\,+\,{\alpha }_1 n\right) , \end{aligned}$$ ∑ n = 1 P e α k n k + α 1 n , involving lower order main terms. As an application, we show that for alm
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d2e04e9db692898fe58153599dc8b454
Publikováno v:
The Quarterly Journal of Mathematics. 68:729-758
Fix $k$ a positive integer, and let $\ell$ be coprime to $k$. Let $p(k,\ell)$ denote the smallest prime equivalent to $\ell \pmod{k}$, and set $P(k)$ to be the maximum of all the $p(k,\ell)$. We seek lower bounds for $P(k)$. In particular, we show th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::98850f182e68a1a6f224d73cde8ded05
https://doi.org/10.1093/qmath/hax001
https://doi.org/10.1093/qmath/hax001
Publikováno v:
The Electronic Journal of Combinatorics. 26
The Van der Waerden number $W(k,r)$ denotes the smallest $n$ such that whenever $[n]$ is $r$–colored there exists a monochromatic arithmetic progression of length $k$. Similarly, the Hilbert cube number $h(k,r)$ denotes the smallest $n$ such that w
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::803ae981344fdffac232c0c51c43dfb1
https://doi.org/10.37236/7917
https://doi.org/10.37236/7917
Autor:
M. B. Erdoğan, George Shakan
Publikováno v:
Selecta Mathematica. 25
We use exponential sums to study the fractal dimension of the graphs of solutions to linear dispersive PDE. Our techniques apply to Schrodinger, Airy, Boussinesq, the fractional Schrodinger, and the gravity and gravity–capillary water wave equation
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::72d901304fb3b1f2a014b99dad08d168
https://doi.org/10.1007/s00029-019-0455-1
https://doi.org/10.1007/s00029-019-0455-1