F. Richter

activity

20122026

most citedA proof of a sumset conjecture of Erdős

32 citations · 208 across the 38 of their papers we have counts for

collaborators

41 papers

math.NT2026

Sum-product patterns in the shifted primes

Florian K. Richter, Joni Teräväinen

We show that the set $P - 1$ of shifted primes contains infinitely many sum-product patterns of the form ${x, x + y, x y}$ with $x, y$ arbitrarily large distinct integers. More…

math.CO2026

Density regularity of ${x, x + y, x y}$ in the integers

Florian K. Richter, Konstantinos Tsinas

Fix $k, s \in N$ . We prove that there exists a subadditive density on $N$ such that, for every polynomial $P \in Z [y]$ of degree $k$ and with $P (0) = 0$ , every…

math.NT2026

Weighted averages of arithmetic functions and applications to equidistribution and ergodic theory

Vitaly Bergelson, Michael Reilly, Florian K. Richter

For a wide range of functions $W : N \to N$ , we establish a general result for estimating weighted averages of the form\[\mathbb{E}^{W}_{n \le N} f(\vartheta(n))…

math.NT2026

An inverse theorem for sumsets of sets of positive density in the integers

Ethan Ackelsberg, Florian K. Richter

Let $d (\cdot)$ denote the natural density on the positive integers. We characterize all sets $A, B$ with positive density satisfying $d (A + B) = d (A) + d (B)$ , under the assumption that th…

cs.CC2026

No Constant-Cost Protocol for Point--Line Incidence

Mika Göös, Nathaniel Harms, Florian K. Richter +1

Alice and Bob are given $n$ -bit integer pairs $(x, y)$ and $(a, b)$ , respectively, and they must decide if $y = a x + b$ . We prove that the randomised communication complexity of this Poi…

stat.ME2026

Regularized Regression by Composition: Identifiability, Structured Penalization, and Statistical Guarantees for Multi-Flow Distributional Models

Safaa K. Kadhem

Regression by composition provides a flexible framework for constructing conditional distributions through sequential group actions. However, when multiple flows act on the same di…

math.DS2026

A short proof of Erdős's $B + C$ conjecture

Bryna Kra, Joel Moreira, Florian K. Richter +1

We give a short proof of the fact that every set of natural numbers with positive upper Banach density contains the sum of two infinite sets. The approach simplifies earlier existi…

math.DS2025

A structure theorem for polynomial return-time sets in minimal systems

Daniel Glasscock, Andreas Koutsogiannis, Anh N. Le +3

We investigate the structure of return-time sets determined by orbits along polynomial tuples in minimal topological dynamical systems. Building on the topological characteristic f…

math.CO2025

Sums and products in sets of positive density

Florian K. Richter

We develop an analytic approach that draws on tools from Fourier analysis and ergodic theory to study Ramsey-type problems involving sums and products in the integers. Suppose $Q$ …

math.DS2025

The Density Finite Sums Theorem

Bryna Kra, Joel Moreira, Florian K. Richter +1

For any set $A$ of natural numbers with positive upper Banach density and any $k \geq 1$ , we show the existence of an infinite set $B \subset N$ and a shift $t \geq 0$ such th…

math.NT2024

Asymptotic independence of $Ω (n)$ and $Ω (n + 1)$ along logarithmic averages

Dimitrios Charamaras, Florian K. Richter

Let $Ω (n)$ denote the number of prime factors of a positive integer $n$ counted with multiplicities. We show that for any bounded functions $a, b : N \to C$ , $$\f…

math.DS2024

Interpolation sets for dynamical systems

Andreas Koutsogiannis, Anh N. Le, Joel Moreira +2

Originating in harmonic analysis, interpolation sets were first studied in dynamics by Glasner and Weiss in the 1980s. A set $S \subset N$ is an interpolation set for a cl…

math.CO2023★ 3 cited

Problems on infinite sumset configurations in the integers and beyond

Bryna Kra, Joel Moreira, Florian K. Richter +1

In contrast to finite arithmetic configurations, relatively little is known about which infinite patterns can be found in every set of natural numbers with positive density. Buildi…

math.DS2023

On the local Fourier uniformity problem for small sets

Adam Kanigowski, Mariusz Lemańczyk, Florian Karl Richter +1

We consider vanishing properties of exponential sums of the Liouville function $λ$ of the form $$ \lim_{H\to\infty}\limsup_{X\to\infty}\frac{1}{\log X}\sum_{m\leq X}\frac{1}{m}\sup…

math.DS2023

On the maximal spectral type of nilsystems

Ethan Ackelsberg, Florian K. Richter, Or Shalom

Let $(G /Γ, R_{a})$ be an ergodic $k$ -step nilsystem for $k \geq 2$ . We adapt an argument of Parry to show that $L^{2} (G /Γ)$ decomposes as a sum of a subspace with discrete spectrum and a…

math.DS2022

A proof of Erdős's $B + B + t$ conjecture

Bryna Kra, Joel Moreira, Florian K. Richter +1

We show that every set $A$ of natural numbers with positive upper density can be shifted to contain the restricted sumset ${b_{1} + b_{2} : b_{1}, b_{2} \in B and b_{1} \neq = b_{2}}$ …

math.DS2022★ 12 cited

Infinite Sumsets in Sets with Positive Density

Bryna Kra, Joel Moreira, Florian K. Richter +1

Motivated by questions asked by Erdos, we prove that any set $A \subset N$ with positive upper density contains, for any $k \in N$ , a sumset $B_{1} + \dots + B_{k}$ , where…

math.CO2021★ 1 cited

A combinatorial proof of a sumset conjecture of Furstenberg

Daniel Glasscock, Joel Moreira, Florian K. Richter

We give a new proof of a sumset conjecture of Furstenberg that was first proved by Hochman and Shmerkin in 2012: if $lo g r / lo g s$ is irrational and $X$ and $Y$ are $\times r$ -…

math.DS2021★ 6 cited

On Katznelson's Question for skew product systems

Daniel Glasscock, Andreas Koutsogiannis, Florian K. Richter

Katznelson's Question is a long-standing open question concerning recurrence in topological dynamics with strong historical and mathematical ties to open problems in combinatorics…

math.NT2020★ 5 cited

Additive and geometric transversality of fractal sets in the integers

Daniel Glasscock, Joel Moreira, Florian K. Richter

By juxtaposing ideas from fractal geometry and dynamical systems, Furstenberg proposed a series of conjectures in the late 1960's that explore the relationship between digit expans…

math.DS2020★ 8 cited

Multiple ergodic averages along functions from a Hardy field: convergence, recurrence and combinatorial applications

Vitaly Bergelson, Joel Moreira, Florian K. Richter

We obtain new results pertaining to convergence and recurrence of multiple ergodic averages along functions from a Hardy field. Among other things, we confirm some of the conjectur…

math.DS2020★ 10 cited

Uniform distribution in nilmanifolds along functions from a Hardy field

Florian K. Richter

We study equidistribution properties of translations on nilmanifolds along functions of polynomial growth from a Hardy field. More precisely, if $X = G /Γ$ is a nilmanifold, $a_1,\ldo…

math.DS2020★ 2 cited

Structure of multicorrelation sequences with integer part polynomial iterates along primes

Andreas Koutsogiannis, Anh N. Le, Joel Moreira +1

Let $T$ be a measure preserving $Z^{ℓ}$ -action on the probability space $(X, B, μ),$ $q_{1}, \dots, q_{m} : R \to R^{ℓ}$ vector polynomials, and $f_0,…

math.DS2020★ 17 cited

Dynamical generalizations of the Prime Number Theorem and disjointness of additive and multiplicative semigroup actions

Vitaly Bergelson, Florian K. Richter

We establish two ergodic theorems which have among their corollaries numerous classical results from multiplicative number theory, including the Prime Number Theorem, a theorem of…

Sum-product patterns in the shifted primes

Density regularity of {x,x+y,xy} in the integers

Weighted averages of arithmetic functions and applications to equidistribution and ergodic theory

An inverse theorem for sumsets of sets of positive density in the integers

No Constant-Cost Protocol for Point--Line Incidence

Regularized Regression by Composition: Identifiability, Structured Penalization, and Statistical Guarantees for Multi-Flow Distributional Models

A short proof of Erdős's B+C conjecture

A structure theorem for polynomial return-time sets in minimal systems

Sums and products in sets of positive density

The Density Finite Sums Theorem

Asymptotic independence of Ω(n) and Ω(n+1) along logarithmic averages

Interpolation sets for dynamical systems

Problems on infinite sumset configurations in the integers and beyond

On the local Fourier uniformity problem for small sets

On the maximal spectral type of nilsystems

A proof of Erdős's B+B+t conjecture

Infinite Sumsets in Sets with Positive Density

A combinatorial proof of a sumset conjecture of Furstenberg

On Katznelson's Question for skew product systems

Additive and geometric transversality of fractal sets in the integers

Multiple ergodic averages along functions from a Hardy field: convergence, recurrence and combinatorial applications

Uniform distribution in nilmanifolds along functions from a Hardy field

Structure of multicorrelation sequences with integer part polynomial iterates along primes

Dynamical generalizations of the Prime Number Theorem and disjointness of additive and multiplicative semigroup actions

Density regularity of ${x, x + y, x y}$ in the integers

A short proof of Erdős's $B + C$ conjecture

Asymptotic independence of $Ω (n)$ and $Ω (n + 1)$ along logarithmic averages

A proof of Erdős's $B + B + t$ conjecture