References
G. H. Hardy, Divergent Series (Oxford Univ. Press, Oxford, 1949).
E. C. Titchmarsh, The Theory of the Riemann Zeta-Function (Clarendon, Oxford, 1951).
E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen (Teubner, Leipzig, 1909).
J. Moser, Jacob’s Ladders, Riemann’s Oscillators, Quotient of the Oscillating Multiforms and Set of Metamorphoses of This System. http://arxiv.org/pdf/1506.00442.pdf.Submitted June 1, 2015.
J. Moser, Jacob’s Ladders, ζ-Factorization and Infinite Set of Metamorphosis of a Multiform. http://arxiv. org/pdf/1501.07705.pdf. Submitted February 10, 2015.
J. Moser, Jacob’s Ladders, New Properties of the Function arg ζ(1/2+ it) and Corresponding Metamorphoses. http://arxiv.org/pdf/1506.07967.pdf. Submitted June 26, 2015.
J. Moser, “Jacob’s ladders and almost exact asymptotic representation of the Hardy–Littlewood integral,” Math. Notes 88, 414–422 (2010). http://arxiv.org/pdf/0901.3973.pdf. Submitted January 26, 2009.
J. Moser, “Jacob’s ladders, structure of theHardy–Littlewood integral and some new class of nonlinear integral equations,” Proc. Steklov Inst. 276, 208–221 (2011). http://arxiv.org/pdf/1103. 0359. pdf. Submitted March 2, 2011.
Leonardo Eulero, Institutionum Calculi Integralis (Petropoli, 1768; Russian transl.: Moscow, Gostekhteorizdat, 1956), Vol. 1.
Author information
Authors and Affiliations
Corresponding author
Additional information
Dedicated to the memory of Anatolii Alekseevich Karatsuba
The text was submitted by the author in English.
Published in Russian in Sovremennye Problemy Matematiki, 2016, Vol. 23, pp. 100–111.
Rights and permissions
About this article
Cite this article
Moser, J. Jacob’s ladders, factorization, and metamorphoses as an appendix to the Riemann functional equation for ζ(s) on the critical line. Proc. Steklov Inst. Math. 296 (Suppl 2), 92–102 (2017). https://doi.org/10.1134/S0081543817030105
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0081543817030105