On irrationality criteria for the Ramanujan summation of certain series

DOI10.1142/s179304212350077xOpenAlexW4321015615MaRDI QIDQ6110504

Suraj Singh Khurana

Publication date: 1 August 2023

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s179304212350077x

zbMATH Keywords

Riemann zeta functionirrationalityRamanujan summation

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Applications of hypergeometric functions (33C90) Special methods of summability (40G99) Irrationality; linear independence over a field (11J72)

Cites Work

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• Arithmetic of linear forms involving odd zeta values
• Ramanujan's summation method
• Asymptotic expansions of the Hurwitz--Lerch zeta function
• Ramanujan summation of divergent series
• Ramanujan summation and the exponential generating function \(\sum_{k=0}^{\infty}\frac{z^{k}}{k!}\zeta'(-k)\)
• Tweaking the Beukers integrals in search of more miraculous irrationality proofs a la Apéry
• A Note on the Irrationality of ζ(2) and ζ(3)
• Criteria for irrationality of Euler’s constant