7
$\begingroup$

It is often asserted that the $j$-invariant was first introduced by Felix Klein. Is there any evidence for this claim? What works of Felix Klein do deal with it? What is the origin of the symbol $j$ used for it? Where it had first appeared?

$\endgroup$
5
$\begingroup$

Felix Klein, Über die Transformation der elliptischen Funktionen und die Auflösung der Gleichungen fünften Grades, Math. Ann. 14,‎ 111-172 (1878-1879).

There is also a slightly earlier brief note in Italian, Sull' equazioni dell' Icosaedro nella risoluzione delle equazioni del quinto grado, Rendiconti Reale Istituto Lombardo, Serie 2, vol. 10, p. 253-255‎ (1877).

Dedekind may have gotten there first, see Dedekind or Klein (p. 67).

Notation: Klein used capital $J$, there is a factor 1728 difference with the $j$-invariant. (Read more about the origin of this factor.)

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.