On the Asymptotics to all Orders of the Riemann Zeta Function and of a Two-Parameter Generalization of the Riemann Zeta Functio

Free Download On the Asymptotics to all Orders of the Riemann Zeta Function and of a Two-Parameter Generalization of the Riemann Zeta Function
by Athanassios S. Fokas, Jonatan Lenells
English | 2022 | ISBN: 1470450984 | 128 Pages | True PDF | 1.06 MB

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).

DONWLOAD FROM RAPIDGATOR
kmvfj.zip.html
DOWNLOAD FROM NITROFLARE
kmvfj.zip
DONWLOAD FROM UPLOADGIG
kmvfj.zip
Fikper
kmvfj.zip.html