Sarah Peluse

activity

20122026

most citedOn the polynomial Szemerédi theorem in finite fields

26 citations · 74 across the 21 of their papers we have counts for

collaborators

23 papers

math.NT2026

Another proof of the $U^{4} (F_{p}^{n})$ -inverse theorem

Sarah Peluse

We give a new and shorter proof of a quantitative inverse theorem for the Gowers $U^{4}$ -norm in the setting of high-dimensional vector spaces over finite fields.

math.DS2024

The multilinear circle method and a question of Bergelson

Dariusz Kosz, Mariusz Mirek, Sarah Peluse +2

Let $k \in Z_{+}$ and $(X, B (X), μ)$ be a probability space equipped with a family of commuting invertible measure-preserving transformations $T_1,\ldots, T_k \colon…

math.NT2024

Bounds in a popular multidimensional nonlinear Roth theorem

Sarah Peluse, Sean Prendiville, Xuancheng Shao

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…

math.NT2023★ 2 cited

Effective bounds for Roth's theorem with shifted square common difference

Sarah Peluse, Ashwin Sah, Mehtaab Sawhney

Let $S$ be a subset of ${1, \dots, N}$ avoiding the nontrivial progressions $x, x + y^{2} - 1, x + 2 (y^{2} - 1)$ . We prove that $∣ S ∣ ≪ N / lo g_{m} N$ , where $lo g_{m}$ is the $m$ -fold iterated…

math.CO2023★ 1 cited

Divisibility of character values of the symmetric group by prime powers

Sarah Peluse, Kannan Soundararajan

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 ea…

math.NT2022★ 3 cited

Polynomial progressions in topological fields

Ben Krause, Mariusz Mirek, Sarah Peluse +1

Let $P_{1}, \dots, P_{m} \in K [y]$ be polynomials with distinct degrees, no constant terms and coefficients in a general locally compact topological field $K$ . We give a quantitative…

math.NT2022★ 1 cited

Recent progress on bounds for sets with no three terms in arithmetic progression

Sarah Peluse

This is the text accompanying my Bourbaki seminar on the work of Bloom and Sisask, Croot, Lev, and Pach, and Ellenberg and Gijswijt.

math.CO2022

Subsets of $F_{p}^{n} \times F_{p}^{n}$ without L-shaped configurations

Sarah Peluse

Fix a prime $p \geq 11$ . We show that there exists a positive integer $m$ such that any subset of $F_{p}^{n} \times F_{p}^{n}$ containing no nontrivial configurations of the…

math.CO2020

Almost all entries in the character table of the symmetric group are multiples of any given prime

Sarah Peluse, Kannan Soundararajan

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.

math.CO2020★ 2 cited

On even entries in the character table of the symmetric group

Sarah Peluse

We show that almost every entry in the character table of $S_{n}$ is even as $n \to \infty$ . This resolves a conjecture of Miller. We similarly prove that almost every entry in the cha…

math.NT2020

An asymptotic version of the prime power conjecture for perfect difference sets

Sarah Peluse

We show that the number of positive integers $n \leq N$ such that $Z / (n^{2} + n + 1) Z$ contains a perfect difference set is asymptotically $N / lo g N$ .

math.NT2020

A polylogarithmic bound in the nonlinear Roth theorem

Sarah Peluse, Sean Prendiville

We show that sets of integers lacking the configuration $x$ , $x + y$ , $x + y^{2}$ have at most polylogarithmic density.

math.NT2019★ 21 cited

Bounds for sets with no polynomial progressions

Sarah Peluse

Let $P_{1}, \dots, P_{m} \in Z [y]$ be polynomials with distinct degrees, each having zero constant term. We show that any subset $A$ of ${1, \dots, N}$ with no nontrivial progress…

math.NT2019★ 2 cited

Quantitative bounds in the nonlinear Roth theorem

Sarah Peluse, Sean Prendiville

We show that there exists $c > 0$ such that any subset of ${1, \dots, N}$ of density at least $(lo g lo g N)^{- c}$ contains a nontrivial progression of the form $x, x + y, x + y^{2}$ . This…

math.NT2018★ 26 cited

On the polynomial Szemerédi theorem in finite fields

Sarah Peluse

Let $P_{1}, \dots, P_{m} \in Z [y]$ be any linearly independent polynomials with zero constant term. We show that there exists a $γ > 0$ such that any subset of $F_{q}$ of siz…

math.NT2017

Three-term polynomial progressions in subsets of finite fields

Sarah Peluse

Bourgain and Chang recently showed that any subset of $F_{p}$ of density $≫ p^{- 1/15}$ contains a nontrivial progression $x, x + y, x + y^{2}$ . We answer a question of theirs by p…

math.CO2016★ 6 cited

Mixing for three-term progressions in finite simple groups

Sarah Peluse

Answering a question of Gowers, Tao proved that any $A \times B \times C \subset S L_{d} (F_{q})^{3}$ contains $|A||B||C|/|SL_d(\mathbb{F}_q)|+O_d(|SL_d(\mathbb{F}_q)|^2/q^{\min(d-1,…

math.NT2016

On exponential sums over orbits in $F_{p}^{d}$

Sarah Peluse

This paper proves a bound for exponential sums over orbits of vectors in $F_{p}^{d}$ under subgroups of $GL_{d} (F_{p})$ . The main tool is a classification theorem fo…

math.CO2015★ 2 cited

Stern Sequences for a Family of Multidimensional Continued Fractions: TRIP-Stern Sequences

Ilya Amburg, Krishna Dasaratha, Laure Flapan +6

The Stern diatomic sequence is closely linked to continued fractions via the Gauss map on the unit interval, which in turn can be understood via systematic subdivisions of the unit…

math.NT2014

Congruence properties of Borcherds product exponents

Keenan Monks, Sarah Peluse, Lynnelle Ye

In his striking 1995 paper, Borcherds found an infinite product expansion for certain modular forms with CM divisors. In particular, this applies to the Hilbert class polynomial of…

math.NT2014★ 3 cited

Strings of special primes in arithmetic progressions

Keenan Monks, Sarah Peluse, Lynnelle Ye

The Green-Tao Theorem, one of the most celebrated theorems in modern number theory, states that there exist arbitrarily long arithmetic progressions of prime numbers. In a related…

math.NT2012★ 2 cited

Cubic Irrationals and Periodicity via a Family of Multi-dimensional Continued Fraction Algorithms

Krishna Dasaratha, Laure Flapan, Thomas Garrity +5

We construct a countable family of multi-dimensional continued fraction algorithms, built out of five specific multidimensional continued fractions, and find a wide class of cubic…

math.NT2012★ 3 cited

A Generalized Family of Multidimensional Continued Fractions: TRIP Maps

Krishna Dasaratha, Laure Flapan, Thomas Garrity +5

Most well-known multidimensional continued fractions, including the Mönkemeyer map and the triangle map, are generated by repeatedly subdividing triangles. This paper constructs a…

Another proof of the U4(Fpn​)-inverse theorem

The multilinear circle method and a question of Bergelson

Bounds in a popular multidimensional nonlinear Roth theorem

Effective bounds for Roth's theorem with shifted square common difference

Divisibility of character values of the symmetric group by prime powers

Polynomial progressions in topological fields

Recent progress on bounds for sets with no three terms in arithmetic progression

Subsets of Fpn​×Fpn​ without L-shaped configurations

Almost all entries in the character table of the symmetric group are multiples of any given prime

On even entries in the character table of the symmetric group

An asymptotic version of the prime power conjecture for perfect difference sets

A polylogarithmic bound in the nonlinear Roth theorem

Bounds for sets with no polynomial progressions

Quantitative bounds in the nonlinear Roth theorem

On the polynomial Szemerédi theorem in finite fields

Three-term polynomial progressions in subsets of finite fields

Mixing for three-term progressions in finite simple groups

On exponential sums over orbits in Fpd​

Stern Sequences for a Family of Multidimensional Continued Fractions: TRIP-Stern Sequences

Congruence properties of Borcherds product exponents

Strings of special primes in arithmetic progressions

Cubic Irrationals and Periodicity via a Family of Multi-dimensional Continued Fraction Algorithms

A Generalized Family of Multidimensional Continued Fractions: TRIP Maps

Another proof of the $U^{4} (F_{p}^{n})$ -inverse theorem

Subsets of $F_{p}^{n} \times F_{p}^{n}$ without L-shaped configurations

On exponential sums over orbits in $F_{p}^{d}$