Cancellation in the Additive Twists of Fourier Coefficients for ${\mathrm{G}\mathrm{L}}_2$ and ${\mathrm{G}\mathrm{L}}_3$ over Number Fields

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