Ideal-Smooth Sets and an Explicit Upper Bound for the Real Sum-Product Exponent

Kaiqiang Zhang, Yuanguo Zeng, Yuyu Wang

We construct arbitrarily large finite sets $A$ of real algebraic integers such that both $|A+A|$ and $|AA|$ are at most $|A{|}^{1.95835}$. The construction combines truncated ideal-s…