40 citations · 118 across the 23 of their papers we have counts for
29 papers
The strong form of Van der Waerden's conjecture via twisted Chowla
Theresa C. Anderson, Sam Chow, Rainer Dietmann +5
Determining the properties of a random polynomial has fuelled significant investigation over the past century. One driving force of this research is a 1936 paper of Van der Waerden…
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…
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…
Rational lines on cubic hypersurfaces II
Julia Brandes, Rainer Dietmann, David B. Leep
We show that any rational cubic hypersurface of dimension at least 33 defined over a number field vanishes on a -rational projective line, reducing the previous lower bound…
Enumerative Galois theory for number fields
Sam Chow, Rainer Dietmann
Counting number fields with prescribed Galois group is an enduring challenge in arithmetic statistics. Using the determinant method, we provide an upper bound for even groups, whic…
Towards van der Waerden's conjecture
Sam Chow, Rainer Dietmann
How often is a quintic polynomial solvable by radicals? We establish that the number of such polynomials, monic and irreducible with integer coefficients in , is $O(H^{3.91…