3 papers
math.AG2025
Generalized connectedness and Bertini-type theorems over real closed fields
Yi Ouyang, Chenhao Zhang
In this paper, we establish a real closed analogue of Bertini's theorem. Let be a real closed field and a formally real integral algebraic variety over . We show that if…
math.NT2025
Finiteness of Pythagoras numbers of finitely generated real algebras
Yi Ouyang, Qimin Song, Chenhao Zhang
In this paper, we establish two finiteness results and propose a conjecture concerning the Pythagoras number of a finitely generated real algebra . Let $X \hookrightarrow…
math.NT2025
On imaginary quadratic fields with non-cyclic class groups
Yi Ouyang, Qimin Song, Chenhao Zhang
For a fixed abelian group , let be the number of square-free positive integers such that H is a subgroup of . We obtain asymptotic…