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pro vyhledávání: '"Peluse, Sarah"'
Let $k\in \mathbb Z_+$ and $(X, \mathcal B(X), \mu)$ be a probability space equipped with a family of commuting invertible measure-preserving transformations $T_1,\ldots, T_k \colon X\to X$. Let $P_1,\ldots, P_k\in\mathbb Z[\rm n]$ be polynomials wit
Externí odkaz:
http://arxiv.org/abs/2411.09478
A nonlinear version of Roth's theorem states that dense sets of integers contain configurations of the form $x$, $x+d$, $x+d^2$. We obtain a multidimensional version of this result, which can be regarded as a first step towards effectivising those ca
Externí odkaz:
http://arxiv.org/abs/2407.08338
We develop a new approach to address some classical questions concerning the size and structure of integer distance sets. Our main result is that any integer distance set in the Euclidean plane has all but a very small number of points lying on a sin
Externí odkaz:
http://arxiv.org/abs/2401.10821
Autor:
Peluse, Sarah
About twenty years ago, Green wrote a survey article on the utility of looking at toy versions over finite fields of problems in additive combinatorics. This article was extremely influential, and the rapid development of additive combinatorics neces
Externí odkaz:
http://arxiv.org/abs/2312.08100
Let $S$ be a subset of $\{1,\ldots,N\}$ avoiding the nontrivial progressions $x, x+y^2-1, x+ 2(y^2-1)$. We prove that $|S|\ll N/\log_m{N}$, where $\log_m $ is the $m$-fold iterated logarithm and $m\in\mathbf{N}$ is an absolute constant. This answers
Externí odkaz:
http://arxiv.org/abs/2309.08359
Autor:
Peluse, Sarah, Soundararajan, Kannan
Proving a conjecture of Miller, we show that as $n$ tends to infinity almost all entries in the character table of $S_n$ are divisible by any given prime power. This extends our earlier work which treated divisibility by primes.
Comment: In memo
Comment: In memo
Externí odkaz:
http://arxiv.org/abs/2301.02203
Let $P_1, \ldots, P_m \in K[y]$ be polynomials with distinct degrees, no constant terms and coefficients in a general locally compact topological field $K$. We give a quantitative count of the number of polynomial progressions $x, x+P_1(y), \ldots, x
Externí odkaz:
http://arxiv.org/abs/2210.00670
Autor:
Peluse, Sarah
Publikováno v:
Ast\'erisque, S\'eminaire Bourbaki. Vol. 2021/2022. Expos\'es 1181--1196(2022), no.438, No. 1196, 581 pp
This is the text accompanying my Bourbaki seminar on the work of Bloom and Sisask, Croot, Lev, and Pach, and Ellenberg and Gijswijt.
Comment: 33 pages; v2: several typos fixed
Comment: 33 pages; v2: several typos fixed
Externí odkaz:
http://arxiv.org/abs/2206.10037
Autor:
Peluse, Sarah
Publikováno v:
Compos. Math., 160(1), 176-236, 2024
Fix a prime $p\geq 11$. We show that there exists a positive integer $m$ such that any subset of $\mathbb{F}_p^n\times\mathbb{F}_p^n$ containing no nontrivial configurations of the form $(x,y),(x,y+z),(x,y+2z),(x+z,y)$ must have density $\ll 1/\log_{
Externí odkaz:
http://arxiv.org/abs/2205.01295
Autor:
Peluse, Sarah, Soundararajan, Kannan
Publikováno v:
J. Reine Angew. Math. 786 (2022), 45-53
We show that almost every entry in the character table of $S_N$ is divisible by any fixed prime as $N\to\infty$. This proves a conjecture of Miller.
Comment: 9 pages, 1 figure; v2: referee suggestions incorporated
Comment: 9 pages, 1 figure; v2: referee suggestions incorporated
Externí odkaz:
http://arxiv.org/abs/2010.12410