A note on odd zeta values. (English) Zbl 1470.11203

Summary: Using a new construction of rational linear forms in odd zeta values [the second author, SIGMA, Symmetry Integrability Geom. Methods Appl. 14, Paper 028, 8 p. (2018; Zbl 1445.11063)] and the saddle point method, we prove the existence of at least two irrational numbers amongst the 33 odd zeta values \(\zeta(5), \zeta (7), \ldots, \zeta (69)\).


11J72 Irrationality; linear independence over a field
11M06 \(\zeta (s)\) and \(L(s, \chi)\)
33C20 Generalized hypergeometric series, \({}_pF_q\)


Zbl 1445.11063
Full Text: arXiv Link


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