Some weeks ago, the Riemann zeta function and the Riemann hypothesis were again in the news. Sir Michael Atiyah proposed a (wrong) failed proof of the Riemann hypothesis. My blog has an history of being controversial from time to time. … Continue reading
Today, I return to my best friends. The polylogs! Are you ready for polylog wars? The polylogarithm can be represented by the next integral: (1) As you know, if you follow my blog, you have … Continue reading
Let me begin this article in D=d+1 spacetime. We are going to study quantum gases and their statistics in multidimensional space. Usual notation: In D=d+1 spacetime, the massless free ideal relativistic gas satisfies, as we will show, certain … Continue reading
In this final post (by the moment) in the polylogia series we will write some additional formulae for polylogs and associated series. Firstly, we have (1) and now, if (2) (3) The next identity also holds … Continue reading
In the third post of this series I will write more fantastic identities related to our friends, the polylogs! (1) and by analytic continuation that equation can be extended to all . In fact (2) such as , … Continue reading
The polylogarithm or Jonquière’s function is generally defined as Do not confuse with the logarithm integral in number theory, which is such as and . In fact, notation can be confusing sometimes … Continue reading
In the next series of post, I am going to define (again) and write some cool identities of several objects that mathematicians and physicists know as zeta functions and polylogarithms. I have talked about them already here http://www.thespectrumofriemannium.com/2012/11/07/log051-zeta-zoology/ 1. We … Continue reading
“(…) The answer to the Great Question…is…Forty-two(…)” said Deep Thought with infinity majesty and calm (frequently found quote from The Hitchhiker’s Guide to the Galaxy, Douglas Adams, London 1979) Dear readers, yesterday, while I was editing, re-editing and writing my … Continue reading
My post today will be discussing two ideas: the primorial and the paper “The product over all primes is “ (2003). The primorial is certain generalization of the factorial, but running on prime numbers. While the factorial is defined as … Continue reading
My second post this day is a beautiful relationship between the Riemann zeta function, the unit hypercube and certain multiple integral involving a “logarithmic and weighted geometric mean”. I discovered it in my rival blog, here: http://tardigrados.wordpress.com/2013/01/08/la-funcion-zeta-de-riemann-definida-en-terminos-de-integrales-multiples/ First of all, … Continue reading