Tuesday, April 2, 2013


Filed under: General,Geometry — Tags: , — m759 @ 7:14 PM

A sequel to the quotation here March 8 (Pinter Play)
of Joan Aiken's novel The Shadow Guests

Supposing that one's shadow guests are
Rosenhain and Göpel (see March 18)

Hans Freudenthal at Encyclopedia.com on Charles Hermite:

"In 1855 Hermite took advantage of Göpel’s and Rosenhain’s work
when he created his transformation theory (see below)."

"One of his invariant theory subjects was the fifth-degree equation,
to which he later applied elliptic functions.

Armed with the theory of invariants, Hermite returned to
Abelian functions. Meanwhile, the badly needed theta functions
of two arguments
had been found, and Hermite could apply what
he had learned about quadratic forms to understanding the
transformation of the system of the four periods. Later, Hermite’s
1855 results became basic for the transformation theory of Abelian
functions as well as for Camille Jordan’s theory of 'Abelian' groups.
They also led to Herrnite’s own theory of the fifth-degree equation
and of the modular equations of elliptic functions. It was Hermite’s
merit to use ω rather than Jacobi’s q = eπω as an argument and to
prepare the present form of the theory of modular functions.
He again dealt with the number theory applications of his theory,
particularly with class number relations or quadratic forms.
His solution of the fifth-degree equation by elliptic functions
(analogous to that of third-degree equations by trigonometric functions)
was the basic problem of this period."

See also Hermite in The Catholic Encyclopedia.

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