LI Lai

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math.NT2025

On the irrationality of certain $p$ -adic zeta values

Li Lai, Cezar Lupu, Johannes Sprang

A famous theorem of Zudilin states that at least one of the Riemann zeta values $ζ (5), ζ (7), ζ (9), ζ (11)$ is irrational. In this paper, we establish the $p$ -adic analogue of Zudili…

math.NT2025

A partial result towards the Chowla--Milnor conjecture

Li Lai, Jia Li

The Chowla--Milnor conjecture predicts the linear independence of certain Hurwitz zeta values. In this paper, we prove that for any fixed integer $k ⩾ 2$ , the dimension of…

math.NT2025

A note on the number of irrational odd zeta values, II

Li Lai

We prove that there are at least $1.284 \cdot s / lo g s$ irrational numbers among $ζ (3)$ , $ζ (5)$ , $ζ (7)$ , $\dots$ , $ζ (s - 1)$ for any sufficiently large even integer $s$ . This…

On the irrationality of certain p-adic zeta values

A partial result towards the Chowla--Milnor conjecture

A note on the number of irrational odd zeta values, II

On the irrationality of certain $p$ -adic zeta values