Polynomial splines interpolating prime series
Number Theory
2007-05-23 v5
Abstract
Differentiable real function reproducing primes up to a given number and having a differentiable inverse function is constructed. This inverse function is compared with the Riemann-Von Mangoldt exact expression for the number of primes not exceeding a given value. Software for computation of the direct and inverse functions and their derivatives is developed. Examples of approximate solution of Diophantine equations on the primes are given.
Cite
@article{arxiv.math/0212246,
title = {Polynomial splines interpolating prime series},
author = {Lumomir Alexandrov and D. B. Baranov and Plamen Yotov},
journal= {arXiv preprint arXiv:math/0212246},
year = {2007}
}
Comments
28 pages, 9 figures, 1 Fortran packages included in source, 2 listings with solutions of Diophantine equations on primes and twins