Titlebook: Elliptic Functions according to Eisenstein and Kronecker; André Weil Book Dec 1998Latest edition Springer-Verlag Berlin Heidelberg 1976 Et

从容

https://doi.org/10.1007/978-3-662-08567-7As in earlier chapters, we write . for a lattice in the complex plane, and ., . for two generators of ., so that . consists of the points ., where . are integers. By . we will denote a character of the additive group . occasionally we shall write . for ..

AUGER

IntroductionIn 1891, Kronecker agreed to give the inaugural lecture at the first meeting of the newly founded German Mathematical Society. He cancelled this plan after losing his wife, but (in a letter to Cantor, president of the society) expressed the hope that he would still be able to supply a written text for the lecture, which he described as follows:

表示问

Variation II§ 1. As we have seen in Chap. IV, Eisenstein’s method provides an easy access to the derivatives ..... with respect to .; this is one of its virtues. Using the results in Chap. III, § 5, one can then exchange . with ., and so obtain formulas for the derivatives with respect to ..

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Prelude to Kronecker§ 1. Kronecker was born in 1823, the same year as Eisenstein; they were students in Berlin at the same time. In 1847 Kronecker had to leave Berlin to take care of the business interests of his family; by the time he came back to settle there permanently, Eisenstein was dead.

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https://doi.org/10.1007/978-3-663-01269-6s of the points ., where . are integers. Then . is not real and may be written as ., where . and τ is in the upper half-plane; sometimes it will be convenient to write . for .. We write ... with . as defined in Chap. II, §7, and we will always take for . the branch given by q.=e(τ/2); we have |q|<1.

大漩涡

Differential- und Integralrechnung,(cf. Chap. II). One cannot, however, apply directly the identity (3) of Chap. II, §2, to the functions .. defined in (3), Chap. III, §2; difficulties of convergence would stand in the way. No such difficulty arises if one starts from the identity (2) of Chap. II, §2, with . 3; this is the procedure

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Differential- und Integralrechnung, Chap. II, § 5), much of Kronecker’s best work consists of such variations, although Kronecker could of course not refrain from adding some themes of his own to Eisenstein’s; this will be discussed in Chap. VII and VIII. In this chapter and the next one, we will stay closer to Eisenstein; as an exam

SPALL

https://doi.org/10.1007/978-3-662-58738-6 to indicate how he wished it completed. Kronecker, having conceived ambitious plans for a vastly enlarged edifice, started, rather late in life, to dig deeper foundations but found time for little else. It is idle to speculate about the kind of continuation he had in mind; perhaps he did not know i