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math.NT2024
Sets with no solutions to some symmetric linear equations
Tomasz Kosciuszko
We expand the class of linear symmetric equations for which large sets with no non-trivial solutions are known. Our idea is based on first finding a small set with no solutions and…
math.NT2023★ 2 cited
Counting solutions to invariant equations in dense sets
Tomasz Kosciuszko
We prove a lower bound of exp(-C (log(2/alpha))^7)N^{k-1} to the number of solutions of an invariant equation in k variables, contained in a set of density alpha. Moreover, we give…