Authors: Pedro Caceres
The Riemann Zeta function or Euler–Riemann Zeta function, ζ(s), is a function of a complex variable z that analytically continues the sum of the Dirichlet series: () = ∑ ^(-z) from k=1,∞ The Riemann zeta function is a meromorphic function on the whole complex z-plane, which is holomorphic everywhere except for a simple pole at z = 1 with residue 1. One of the most important advance in the study of Prime numbers was the paper by Bernhard Riemann in November 1859 called “Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse” (On the number of primes less than a given quantity). In this paper, Riemann gave a formula for the number of primes less than x in terms the integral of 1/log(x), and also provided insights into the roots (zeros) of the zeta function, formulating a conjecture about the location of the zeros of () in the critical line Re(z)=1/2. The Riemann Zeta function is one of the most studied and well known mathematical functions in history. In this paper, we will formulate nine new propositions to advance in the knowledge of the Riemann Zeta function
Comments: 27 Pages.
[v1] 2019-04-19 21:33:45
Unique-IP document downloads: 34 times
Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.