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Rado's criterion over squares and higher powers
Sam Chow, Sofia Lindqvist, Sean Prendiville
We establish partition regularity of the generalised Pythagorean equation in five or more variables. Furthermore, we show how Rado's characterisation of a partition regular equatio…
Full Orbit Sequences in Affine Spaces via Fractional Jumps and Pseudorandom Number Generation
Federico Amadio Guidi, Sofia Lindqvist, Giacomo Micheli
Let be a positive integer. In this paper we provide a general theory to produce full orbit sequences in the affine -dimensional space over a finite field. For our cons…
Weak approximation results for quadratic forms in four variables
Sofia Lindqvist
Let be a quadratic form in four variables, let and let . We count integer solutions to with $\mathbf{x}\equiv \ma…
Monochromatic solutions to
Ben Green, Sofia Lindqvist
Suppose that is -coloured. Then there are infinitely many monochromatic solutions to . On the other hand, there is a -colouring of with…
Partition regularity of generalised Fermat equations
Sofia Lindqvist
Let . We prove that given an -colouring of with prime, there are more than solutions to the equation with…
Moments of random multiplicative functions and truncated characteristic polynomials
Winston Heap, Sofia Lindqvist
We give an asymptotic formula for the th moment of a sum of multiplicative Steinhaus variables. This was recently computed independently by Harper, Nikeghbali and Radziwiłł. We…