Abstract
The publications that Dirichlet offered from late 1839 until his travel to Italy in 1843 had a common theme. It was that of progressing on the new pathways opened as the result of his reflecting on the successful technique he had applied to the proof of the theorem on arithmetic progressions. He wished to explore further the possibilities of linking number-theoretic questions to infinitesimal analysis, in particular, the use of his L-series and functions, suggested by Euler’s Chapter 15 of the Introduction to Analysis of the Infinite [Euler 1748].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Legendre 1830, vol. 2 finally had incorporated significant parts of Section 7 (cyclotomy) of Gauss’s D.A., but still lacked some of the necessary proofs.
- 2.
Werke 1:413–14.
- 3.
Legendre 1808: preface.
- 4.
Werke 1:414.
- 5.
Kronecker 1865:285; see Kronecker Werke 4:229.
- 6.
A reprint of the 1801 edition appeared in volume 1 (1863, reprinted in 1870) of Gauss’s collected works. Until 1889, when the first German translation appeared, there were no other editions of the D.A. besides those mentioned. For lists of subsequent editions and translations, see Merzbach 1984:1, 3, 44–45, 47, 49–52, or the later Goldstein et al., eds, 2010:xi, which, in addition to a 1989 reprint of the French translation, includes Spanish, Japanese, and Catalan translations published in the 1990s.
- 7.
Werke 1:414–15.
- 8.
Werke 1:415–16.
- 9.
See Werke 1:500–502.
- 10.
Gauss D.A., end of art. 306.VI.
- 11.
Legendre 1830, 2:102–3.
- 12.
See the sharply critical assessment of this work by Legendre in Weil 1983:329–30.
- 13.
See Bachmann 1894/1921:272.
- 14.
Tannery 1910:2–3; translated in Lützen 1990:61.
- 15.
Werke 1:621.
- 16.
Werke 1:622.
- 17.
Werke 1:623.
- 18.
This larger work would become 1842b.
- 19.
Werke 1:507.
- 20.
Werke 1:627.
- 21.
Dirichlet here used the term “group” in an informal (non-mathematical) sense.
- 22.
Werke 1:635.
- 23.
Note that the intervals serve as Schubfächer, and this is a clear application of the “pigeonhole principle.” See Chapter 1 of Minkowski 1907.
- 24.
Also see 1840d.
- 25.
Minkowski 1907:1.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Merzbach, U.C. (2018). Publications: 1839–1845. In: Dirichlet. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-01073-7_11
Download citation
DOI: https://doi.org/10.1007/978-3-030-01073-7_11
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-01071-3
Online ISBN: 978-3-030-01073-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)