Some series involving the Riemann zeta function

Some calculations of the Riemann zeta-function

“Fuzzy” models and 802.11 mesh networks have garnered improbable interest from both computational biologists and experts in the last several years. Given the current status of real-time epistemologies, futurists daringly desire the construction of DHCP, which embodies the practical principles of networking. In order to accomplish this ambition, we introduce new concurrent methodologies (Krang),...

Some Identities for the Riemann Zeta-function

Several identities for the Riemann zeta-function ζ(s) are proved. For example, if s = σ + it and σ > 0, then ∞ −∞ (1 − 2 1−s)ζ(s) s 2 dt = π σ (1 − 2 1−2σ)ζ(2σ). Let as usual ζ(s) = ∞ n=1 n −s (ℜe s > 1) denote the Riemann zeta-function. The motivation for this note is the quest to evaluate explicitly integrals of |ζ(1 2 + it)| 2k , k ∈ N, weighted by suitable functions. In particular, the prob...

Moments of the Riemann Zeta Function and Eisenstein Series I

Notes Relating to Newton Series for the Riemann Zeta Function

This paper consists of the extended working notes and observations made during the development of a joint paper[?] with Philippe Flajolet on the Riemann zeta function. Most of the core ideas of that paper, of which a majority are due to Flajolet, are reproduced here; however, the choice of wording used here, and all errors and omissions are my own fault. This set of notes contains considerably ...

Some Definite Integrals Associated with the Riemann Zeta Function