Ouyang Yi

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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 $P (A)$ of a finitely generated real algebra $A$ . 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 $H$ , let $N_{H} (X)$ be the number of square-free positive integers $d \leq X$ such that H is a subgroup of $C L (Q (- d))$ . We obtain asymptotic…

math.NT2024

Divisibility of class numbers of quadratic fields and a conjecture of Iizuka

Yi Ouyang, Qimin Song

Assume $x, y, n$ are positive integers and $n$ is odd. In this note, we show that the class number of the imaginary quadratic field $Q (x^{2} - y^{n})$ is divisible…