# Hypergeometric rational approximations to ζ(4)

@article{Marcovecchio2020HypergeometricRA, title={Hypergeometric rational approximations to $\zeta$(4)}, author={Raffaele Marcovecchio and Wadim Zudilin}, journal={Proceedings of the Edinburgh Mathematical Society}, year={2020}, volume={63}, pages={374 - 397} }

Abstract We give a new hypergeometric construction of rational approximations to ζ(4), which absorbs the earlier one from 2003 based on Bailey's 9F8 hypergeometric integrals. With the novel ingredients we are able to gain better control of the arithmetic and produce a record irrationality measure for ζ(4).

#### 2 Citations

Complex hypergeometric functions and integrable many body problems

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- 2021

A classical integrable N -body system representing a relativistic generalization of the Calogero and Sutherland models has been suggested by Ruijsenaars and Schneider [20]. Its quantization… Expand

A case study for $\zeta(4)$

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Using symbolic summation tools in the setting of difference rings, we prove a two-parametric identity that relates rational approximations to $\zeta(4)$.

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