Nine Chapters of Analytic Number Theory in Isabelle/HOL

by Manuel Eberl

In: Proceedings of ITP 2019




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 ζ 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 ω function, the divisor count σ0(n), and Euler's totient function φ(n)

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author="Eberl, Manuel",
title="Nine Chapters of Analytic Number Theory in {I}sabelle/{HOL}",
publisher="Leibniz International Proceedings in Informatics",
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",
volume =	"141",
editor =	"John Harrison and John O'Leary and Andrew Tolmach",
publisher =	"Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik",
address =	{"Dagstuhl, Germany"

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