Hypergeometric series and irrationality of the values of the Riemann zeta function
The author presents a survey of the ideas around his striking discoveries about the values of the Riemann zeta-function at the odd integers. He shows how hypergeometric series and Padé approximants provide a common approach to Apéry's theorem on the irrationality of \(\zeta(3)\), the author's remarkable proof that infinitely many of the \(\zeta(2n+1)\) are irrational, and Zudilin's theorem, improving another result of the author, that at least one of the numbers \(\zeta(5),\zeta(7),\zeta(9),\zeta(11)\) is irrational. Some teasing questions are added in the conclusion.
scientific article; zbMATH DE number 2058873
scientific article