History of the Theory of Numbers

978-0-486-44232-7 (vol.1)
ISBN 978-0-486-44233-4(vol.2)
ISBN 978-0-486-44234-1(vol.3)

History of the Theory of Numbers is a three-volume work by Leonard Eugene Dickson summarizing work in number theory up to about 1920. The style is unusual in that Dickson mostly just lists results by various authors, with little further discussion. The central topic of quadratic reciprocity and higher reciprocity laws is barely mentioned; this was apparently going to be the topic of a fourth volume that was never written (Fenster 1999).

Volumes

• Volume 1 - Divisibility and Primality - 486 pages
• Volume 2 - Diophantine Analysis - 803 pages
• Volume 3 - Quadratic and Higher Forms - 313 pages

References

• Carmichael, Robert D. (1919), "Recent Publications: Reviews: History of the Theory of Numbers. Volume I: Divisibility and Primality", The American Mathematical Monthly, 26 (9): 396–403, doi:10.2307/2971917, ISSN 0002-9890, JSTOR 2971917
• Carmichael, Robert D. (1921), "Recent Publications: Reviews: History of the Theory of Numbers: History of the Theory of Numbers", The American Mathematical Monthly, 28 (2): 72–78, doi:10.2307/2973042, ISSN 0002-9890, JSTOR 2973042
• Carmichael, Robert D. (1923), "Recent Publications: Reviews: History of the Theory of Numbers", The American Mathematical Monthly, 30 (5): 259–262, doi:10.2307/2299094, ISSN 0002-9890, JSTOR 2299094
• Dickson, Leonard Eugene (2005) [1919], History of the theory of numbers. Vol. I: Divisibility and primality., New York: Dover Publications, ISBN 978-0-486-44232-7, MR 0245499, Zbl 1214.11001
• Dickson, Leonard Eugene (2005) [1920], History of the theory of numbers. Vol. II: Diophantine analysis, New York: Dover Publications, ISBN 978-0-486-44233-4, MR 0245500, Zbl 1214.11002
• Dickson, Leonard Eugene (2005) [1923], History of the theory of numbers. Vol. III: Quadratic and higher forms, New York: Dover Publications, ISBN 978-0-486-44234-1, MR 0245501
• Fenster, Della D. (1999), "Leonard Dickson's History of the theory of numbers: an historical study with mathematical implications", Revue d'Histoire des Mathématiques. Journal for the History of Mathematics, 5 (2): 159–179, ISSN 1262-022X, MR 1793101
• Fenster, Della Dumbaugh (1999), "Why Dickson left quadratic reciprocity out of his History of the theory of numbers", The American Mathematical Monthly, 106 (7): 618–627, doi:10.2307/2589491, ISSN 0002-9890, JSTOR 2589491, MR 1720467
• Furtwängler, Ph. (1923), "Literaturberichte: History of the theory of numbers", Monatshefte für Mathematik und Physik, 33 (1): A6–A7, doi:10.1007/BF01705606, ISSN 0026-9255, S2CID 116618046
• Lehmer, D. H. (1919), "Book Review: History of the Theory of Numbers", Bulletin of the American Mathematical Society, 26 (3): 125–132, doi:10.1090/S0002-9904-1919-03280-7, ISSN 0002-9904
• Lehmer, D. H. (1920), "Dickson's history of the theory of numbers", Bulletin of the American Mathematical Society, 26 (6): 281–282, doi:10.1090/S0002-9904-1920-03305-7, ISSN 0002-9904
• Vandiver, H. S. (1924), "Book Review: History of the Theory of Numbers", Bulletin of the American Mathematical Society, 30 (1): 65–70, doi:10.1090/S0002-9904-1924-03852-X, ISSN 0002-9904

External links

• History of the Theory of Numbers - Volume 1 at the Internet Archive.
• History of the Theory of Numbers - Volume 2 at the Internet Archive.
• History of the Theory of Numbers - Volume 3 at the Internet Archive.