On special Riemann xi function formulae of Hardy involving the digamma function

DOI10.14232/ACTASM-020-664-3zbMath1474.11147arXiv1702.05635OpenAlexW3028450507MaRDI QIDQ4997648

Alexander E. Patkowski

Publication date: 29 June 2021

Published in: Acta Scientiarum Mathematicarum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.05635

zbMATH Keywords

Fourier integralsdigamma functionRiemann xi function

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15)

Cites Work

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• Self-reciprocal functions, powers of the Riemann zeta function and modular-type transformations
• Fourier transforms of positive definite kernels and the Riemann \(\xi\)-function
• Riesz-type criteria and theta transformation analogues
• Zeros of combinations of the Riemann \(\xi\)-function on bounded vertical shifts
• Some completely monotonic functions involving polygamma functions and an application
• Analogues of the general theta transformation formula
• A note on the Fourier transform
• Some Solutions of the Equation F (t ) = F (t ⁻¹ )

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