License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITP.2019.16
URN: urn:nbn:de:0030-drops-110714
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11071/
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Eberl, Manuel

Nine Chapters of Analytic Number Theory in Isabelle/HOL

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LIPIcs-ITP-2019-16.pdf (0.5 MB)

Abstract

In this paper, I present a formalisation of a large portion of Apostol's Introduction to Analytic Number Theory in Isabelle/HOL. Of the 14 chapters in the book, the content of 9 has been mostly formalised, while the content of 3 others was already mostly available in Isabelle before.
The most interesting results that were formalised are:
- The Riemann and Hurwitz zeta functions and the Dirichlet L functions
- Dirichlet's theorem on primes in arithmetic progressions
- An analytic proof of the Prime Number Theorem
- The asymptotics of arithmetical functions such as the prime omega function, the divisor count sigma_0(n), and Euler's totient function phi(n)

BibTeX - Entry

@InProceedings{eberl:LIPIcs:2019:11071,
  author =	{Manuel Eberl},
  title =	{{Nine Chapters of Analytic Number Theory in Isabelle/HOL}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{16:1--16:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-122-1},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{141},
  editor =	{John Harrison and John O'Leary and Andrew Tolmach},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/11071},
  URN =		{urn:nbn:de:0030-drops-110714},
  doi =		{10.4230/LIPIcs.ITP.2019.16},
  annote =	{Keywords: Isabelle, theorem proving, analytic number theory, number theory, arithmetical function, Dirichlet series, prime number theorem, Dirichlet's theorem,}
}

Keywords: Isabelle, theorem proving, analytic number theory, number theory, arithmetical function, Dirichlet series, prime number theorem, Dirichlet's theorem,
Collection: 10th International Conference on Interactive Theorem Proving (ITP 2019)
Issue Date: 2019
Date of publication: 05.09.2019
Supplementary Material: The proof developments in the Archive of Formal Proofs (AFP) that this work refers to are listed in the bibliography. Additionally, a precise overview of what material from the book has been formalised and which theorems in the book correspond to which theorems in the formalisation can be found at https://doi.org/10.5281/zenodo.3262266.

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