Polynomial splines interpolating prime series

Details Polynomial splines interpolating prime series Polynomial splines interpolating prime series

2002-12-18

arxiv.org/abs/math/0212246v5

Mathematics

Number Theory

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

Scientific paper

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.

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