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math.NT2021
At least two of are irrational
Li Lai, Li Zhou
Let be the Riemann zeta function. We prove the statement in the title, which improves a recent result of Rivoal and Zudilin by lowering to . We also prove that at l…
math.NT2009★ 14 cited
Recurrent proofs of the irrationality of certain trigonometric values
Li Zhou, Lubomir Markov
We use recurrences of integrals to give new and elementary proofs of the irrationality of pi, tan(r) for all nonzero rational r, and cos(r) for all nonzero rational r^2. Immediate…
math.NT2009★ 2 cited
Irrationality proofs à la Hermite
Li Zhou
As rewards of reading two great papers of Hermite from 1873, we trace the historical origin of the integral Niven used in his well-known proof of the irrationality of , uncover…