Authors: Simon Plouffe
An analysis of the function 1/π Arg ζ((1/2)+in) is presented. This analysis permits to find a general expression for that function using elementary functions of floor and fractional part. These formulas bring light to a remark from Freeman Dyson which relates the values of the ζfunction to quasi-crystals. We find these same values for another function which is very similar, namely 1/π Arg Γ((1/4)+in/2). These 2 sets of formula have a definite pattern, the n’th term is related to values like π,ln(π),ln(2),…,log(p), where p is a prime number. The coefficients are closed related to a certain sequence of numbers which counts the number of 0’s from the right in the binary representation of n. These approximations are regular enough to deduce an asymptotic and precise formula. All results presented here are empirical.
Comments: 13 Pages. The abstract in english and the main text in french
[v1] 2014-08-26 22:24:59
Unique-IP document downloads: 233 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.