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On The Asymptotics To All Orders Of The Riemann Zeta Function And Of A Twoparameter Generalization Of The Riemann Zeta Function Athanassios S Fokas

  • SKU: BELL-48041508
On The Asymptotics To All Orders Of The Riemann Zeta Function And Of A Twoparameter Generalization Of The Riemann Zeta Function Athanassios S Fokas
$ 31.00 $ 45.00 (-31%)

4.1

60 reviews

On The Asymptotics To All Orders Of The Riemann Zeta Function And Of A Twoparameter Generalization Of The Riemann Zeta Function Athanassios S Fokas instant download after payment.

Publisher: American Mathematical Society
File Extension: PDF
File size: 1.06 MB
Pages: 128
Author: Athanassios S. Fokas, Jonatan Lenells
ISBN: 9781470450984, 1470450984
Language: English
Year: 2022

Product desciption

On The Asymptotics To All Orders Of The Riemann Zeta Function And Of A Twoparameter Generalization Of The Riemann Zeta Function Athanassios S Fokas by Athanassios S. Fokas, Jonatan Lenells 9781470450984, 1470450984 instant download after payment.

We present several formulae for the large t asymptotics of the Riemann zeta function ζ(s), s = σ + it, 0 ≤ σ ≤ 1, t > 0, which are valid to all orders. A particular case of these results coincides with the classical results of Siegel. Using these formulae, we derive explicit representations for the sum b a n − s for certain ranges of a and b. In addition, we present precise estimates relating this sum with the sum d c n s − 1 for certain ranges of a, b, c, d. We also study a two-parameter generalization of the Riemann zeta function which we denote by Φ(u, v, β), u ∈ C , v ∈ C , β ∈ R . Generalizing the methodology used in the study of ζ(s), we derive asymptotic formulae for Φ(u, v, β).

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