Arithmetic of Catalan's constant and its relatives

31 May 2019 Zudilin Wadim

We prove that at least one of the six numbers $\beta(2i)$ for $i=1,\dots,6$ is irrational. Here $\beta(s)=\sum_{k=0}^\infty(-1)^k(2k+1)^{-s}$ denotes Dirichlet's beta function, so that $\beta(2)$ is Catalan's constant...

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Categories


  • NUMBER THEORY
  • CLASSICAL ANALYSIS AND ODES
  • COMBINATORICS