Many odd zeta values are irrational

@article{Fischler2018ManyOZ,
  title={Many odd zeta values are irrational},
  author={St'ephane Fischler and Johannes Sprang and W. Zudilin},
  journal={Compositio Mathematica},
  year={2018},
  volume={155},
  pages={938-952}
}
  • St'ephane Fischler, Johannes Sprang, W. Zudilin
  • Published 2018
  • Mathematics
  • Compositio Mathematica
  • Building upon ideas of the second and third authors, we prove that at least $2^{(1-\unicode[STIX]{x1D700})(\log s)/(\text{log}\log s)}$ values of the Riemann zeta function at odd integers between 3 and $s$ are irrational, where $\unicode[STIX]{x1D700}$ is any positive real number and $s$ is large enough in terms of $\unicode[STIX]{x1D700}$ . This lower bound is asymptotically larger than any power of $\log s$ ; it improves on the bound $(1-\unicode[STIX]{x1D700})(\log s)/(1+\log 2)$ that… CONTINUE READING

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