Abstract
In the following we would like to add a few historical remarks on the proofs listed in the First Part.
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Notes
- 1.
The proof by Pépin [62] unfortunately was not accessible to me.
- 2.
[FL] The correspondence between Jacobi and Legendre was published by Pieper: Korrespondenz Adrien-Marie Legendre – Carl Gustav Jacob Jacobi, Teubner 1998.
- 3.
[FL] “two other proofs”
- 4.
[FL] Here then is the third complete proof of the fundamental theorem of Chap. IV.
- 5.
The preceding remarks explain why certain proofs in Table 14.1 do not have a number.
- 6.
[FL] See F. Lemmermeyer, H. Pieper, Jacobis Vorlesungen über Zahlentheorie, Rauner Verlag Augsburg, 2007.
- 7.
[FL] This is the simplest among all known proofs of this fundamental proposition.
Bibliography
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G. Eisenstein, Beiträge zur Theorie der elliptischen Funktionen VI, Genaue Untersuchung der unendlichen Doppelprodukte, aus welchen die elliptischen Functionen als Quotienten zusammengesetzt sind, J. Reine Angew. Math. 35 (1847), 153–274; Math. Werke I, 457–478; cf. p.
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Baumgart, O. (2015). Final Comments. In: The Quadratic Reciprocity Law. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-16283-6_14
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