Cancellation in the additive twists of Fourier coefficients for GL2 and GL3 over number fields

In this article, we study the sum of additively twisted Fourier coefficients of an irreducible cuspidal automorphic representation of ${\rm GL}_2$ or ${\rm GL}_3$ over an arbitrary number field. When the representation is unramified at all non-archimedean places, we prove the Wilton type bound for ${\rm GL}_2$ and the Miller type bound for ${\rm GL}_3$ which are uniform in terms of the additive character.