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)
@InProceedings{eberl:LIPIcs.ITP.2019.16, author = {Eberl, Manuel}, 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 = {Harrison, John and O'Leary, John and Tolmach, Andrew}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2019.16}, 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, zeta function, L functions} }
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