18 citations · 60 across the 29 of their papers we have counts for
40 papers
Two dimensional arithmetic progressions avoiding squares
Rainer Dietmann, Christian Elsholtz
We show that any proper symmetric two dimensional arithmetic progression contained in the interval which avoids non-zero perfect squares has at most $O_\varepsilon(T^{20/2…
There are infinitely many Hilbert cubes of dimension 3 in the set of squares
Andrew Bremner, Christian Elsholtz, Maciej Ulas
A Hilbert cube of dimension is the set of integers \[ H(a_{0}; a_{1}, \ldots, a_{d})=a_{0}+\{0, a_{1}\}+\cdots+\{0, a_{d}\}=\left\{a_{0}+\sum_{i=1}^{d}\varepsilon_{i}a_{i}:\;\v…
Sieving with square conditions and applications to Hilbert cubes in arithmetic sets
Rainer Dietmann, Christian Elsholtz, Imre Ruzsa
The purpose of this paper is twofold: 1) Applications of Gallagher's larger sieve modulo prime squares do not work. In some relevant cases we can transform the residue class inform…
Problems 66 and 67 on sums of residue classes and primes of András Sárközy's collection of unsolved problems
Yuchen Ding, Christian Elsholtz, Yu-Chen Sun
In this note, we discuss two problems of Sárközy (2001). In particular, we prove an optimal result on sumsets of sparse subset of primes.
Improving Behrend's construction: Sets without arithmetic progressions in integers and over finite fields
Christian Elsholtz, Zach Hunter, Laura Proske +1
We prove new lower bounds on the maximum size of subsets or not containing three-term arithmetic progressions. In the setting…
New lower bounds for three-term progression free sets in
Christian Elsholtz, Laura Proske, Lisa Sauermann
We prove new lower bounds on the maximum size of sets or not containing three-term arithmetic progressions (consisting of th…