Polynomial splines interpolating prime series

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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.
28 pages, 9 figures, 1 Fortran packages included in source, 2 listings with solutions of Diophantine equations on primes and twins

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Number Theory, 11N05, 11M20, 65D07

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http://salesiana.dossiersoluciones.com/handle/123456789/66025

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0212246
 http://arxiv.org/abs/math/0212246

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arXiv