About the formalization of some results by Chebyshev in number theory (2009)
| Venue: | Proceedings of TYPES’08, Vol. 5497 of LNCS |
| Citations: | 7 - 3 self |
BibTeX
@INPROCEEDINGS{Asperti09aboutthe,
author = {Andrea Asperti and Wilmer Ricciotti and Mura Anteo Zamboni},
title = {About the formalization of some results by Chebyshev in number theory},
booktitle = {Proceedings of TYPES’08, Vol. 5497 of LNCS},
year = {2009},
publisher = {Springer-Verlag}
}
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Abstract
Abstract. We discuss the formalization, in the Matita Interactive Theorem Prover, of a famous result by Chebyshev concerning the distribution of prime numbers, essentially subsuming, as a corollary, Bertrand’s postulate. Even if Chebyshev’s result has been later superseded by the stronger prime number theorem, his machinery, and in particular the two functions ψ and θ still play a central role in the modern development of number theory. Differently from other recent formalizations of other results in number theory, our proof is entirely arithmetical. It makes use of most part of the machinery of elementary arithmetics, and in particular of properties of prime numbers, factorization, products and summations, providing a natural benchmark for assessing the actual development of the arithmetical knowledge base. 1
Citations
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