2 papers
math.NT2026
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 of real algebraic integers such that both and are at most . The construction combines truncated ideal-s…
math.CO2026
A Refined Sum-Product Estimate via Higher Energies
Kaiqiang Zhang, Yuyu Wang, Yuanguo Zeng
Let be a finite set. Combining the multiplicative slope estimate of Rudnev--Stevens, Cushman's higher-energy regularization, Shakan's -- decompo…