An enveloping series for the zeta function

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 ...

Scattering for Time Series with an Application to the Zeta Function of an Algebraic Curve

I explain how the Lax-Phillips theory can be applied to a purely innovating time series and compute the corresponding scattering function. I then associate such a time series to an algebraic curve (of genus at least 1) over a finite field and show that the Riemann Hypothesis (proven long ago) holds if and only if the scattering is causal (this causality is not independently established, though).

Moments of the Riemann Zeta Function and Eisenstein Series I

Hypergeometric Series Associated with the Hurwitz-lerch Zeta Function

The present work is a sequel to the papers [3] and [4], and it aims at introducing and investigating a new generalized double zeta function involving the Riemann, Hurwitz, Hurwitz-Lerch and Barnes double zeta functions as particular cases. We study its properties, integral representations, differential relations, series expansion and discuss the link with known results.

Rapidly Convergent Series for the Weierstrass Zeta-function and the Kronecker Function

We present expressions for the Weierstrass zeta-function and related elliptic functions by rapidly convergent series. These series arise as triple products in the A∞-category of an elliptic curve. 1. Formulas In this section we derive our formulas by classical means. In the next section we’ll explain how one can guess these formulas from the computation of certain triple products on elliptic cu...