Zobrazeno 1 - 10
of 88
pro vyhledávání: '"Stevens, Sophie"'
Autor:
Mohammadi, Ali, Stevens, Sophie
We improve the exponent in the finite field sum-product problem from $11/9$ to $5/4$, improving the results of Rudnev, Shakan and Shkredov. That is, we show that if $A\subset \mathbb{F}_p$ has cardinality $|A|\ll p^{1/2}$ then \[ \max\{|A\pm A|,|AA|\
Externí odkaz:
http://arxiv.org/abs/2103.08252
Autor:
Stevens, Sophie, Warren, Audie
In this paper we prove new bounds for sums of convex or concave functions. Specifically, we prove that for all $A,B \subseteq \mathbb R$ finite sets, and for all $f,g$ convex or concave functions, we have $$|A + B|^{38}|f(A) + g(B)|^{38} \gtrsim |A|^
Externí odkaz:
http://arxiv.org/abs/2102.05446
Autor:
Mohammadi, Ali, Stevens, Sophie
We prove various low-energy decomposition results, showing that we can decompose a finite set $A\subset \mathbb{F}_p$ satisfying $|A|
Externí odkaz:
http://arxiv.org/abs/2102.01655
In this paper we give a conditional improvement to the Elekes-Szab\'{o} problem over the rationals, assuming the Uniformity Conjecture. Our main result states that for $F\in \mathbb{Q}[x,y,z]$ belonging to a particular family of polynomials, and any
Externí odkaz:
http://arxiv.org/abs/2009.13258
Autor:
Rudnev, Misha, Stevens, Sophie
Publikováno v:
Math. Proc. Cambridge Phil. Soc. 2021
We improve the best known sum-product estimates over the reals. We prove that \[ \max(|A+A|,|AA|)\geq |A|^{\frac{4}{3} + \frac{2}{1167} - o(1)}\,, \] for a finite $A\subset \mathbb R$, following a streamlining of the arguments of Solymosi, Konyagin a
Externí odkaz:
http://arxiv.org/abs/2005.11145
Publikováno v:
J. Lond. Math. Soc.(2) 105 (1), 469-499, 2022
We study the Erd\H os-Falconer distance problem for a set $A\subset \mathbb{F}^2$, where $\mathbb{F}$ is a field of positive characteristic $p$. If $\mathbb{F}=\mathbb{F}_p$ and the cardinality $|A|$ exceeds $p^{5/4}$, we prove that $A$ determines an
Externí odkaz:
http://arxiv.org/abs/2003.00510
We prove a new lower bound for the number of pinned distances over finite fields: if $A$ is a sufficiently small subset of $\mathbb{F}_q^2$, then there is an element in $A$ that determines $\gg |A|^{2/3}$ distinct distances to other elements of $A$.
Externí odkaz:
http://arxiv.org/abs/1908.04618
Autor:
Stevens, Sophie, de Zeeuw, Frank
We prove a new upper bound for the number of incidences between points and lines in a plane over an arbitrary field $\mathbb{F}$, a problem first considered by Bourgain, Katz and Tao. Specifically, we show that $m$ points and $n$ lines in $\mathbb{F}
Externí odkaz:
http://arxiv.org/abs/1609.06284
We prove new exponents for the energy version of the Erd\H{o}s-Szemer\'edi sum-product conjecture, raised by Balog and Wooley. They match the previously established milestone values for the standard formulation of the question, both for general field
Externí odkaz:
http://arxiv.org/abs/1607.05053
Akademický článek
Tento výsledek nelze pro nepřihlášené uživatele zobrazit.
K zobrazení výsledku je třeba se přihlásit.
K zobrazení výsledku je třeba se přihlásit.