The so-called Renormalization Group method applied to the specific prime numbers logarithmic decrease

The So-called Renormalization Group Method Applied to the Specific Prime Numbers Logarithmic Decrease

A so-called Renormalization Group (RG) analysis is performed in order to shed some light on why the density of prime numbers in N decreases like the single power of the inverse neperian logarithm. CERN–TH/2000–146 May 2000 Part I The most elementary proof of the Prime Numbers Theorem These few lines are not part of the proof. They simply show the history which has led to the starting point of o...

The Renormalization-group Method Applied to Non-equilibrium Dynamics

We review the renormalization group method applied to non-equilibrium dynamics by tracing the way how the hydrodynamic equations can be derived as reduced dynamics of the Boltzmann equation as a typical example.

Prime Numbers in Logarithmic Intervals

Let X be a large parameter. We will first give a new estimate for the integral moments of primes in short intervals of the type (p, p+ h], where p ≤ X is a prime number and h = o(X). Then we will apply this to prove that for every λ > 1/2 there exists a positive proportion of primes p ≤ X such that the interval (p, p+λ logX] contains at least a prime number. As a consequence we improve Cheer an...

The So-called Fibonacci Numbers in Ancient and Medieval India

What are generally referred to as the Fibonacci numbers and the method for their formation were given by Virahanka (between A.D. 600 and X00). Gopala (prior to A.D. 1135) and Hemacandra (c. A.D. 1150). all prior to L. Fibonacci (c. A.D. 1202). Narayana Pandita (A.D. 13Sh) established a relation between his srftcisi~ci-pcrirLfi. which contains Fibonacci numbers as a particular case. and “the mul...

Renormalization Group Method Applied to Large Scale Langmuir Turbulence