F. Cajori gives several pointers in his A history of mathematical notations, Vol. 2, page 40. I think (he's a bit unclear...) he attributes the notation to Kronecker, referring to Dickson's History, Vol. 3, page 93. Dickson, in turn, in page 138 of that volume, tells us that Kronecker uses that notation in [Sitzungsberichte Akad. d. Wissensch. (Berlin, 1885), Vol. II, p. 768-80]

He apparently had introduced numbers $F(d)$, $G(d)$, $E(d)$, and when he needed one more, he used $H$ :P

(Reading on, we find the first appearence of a lowercase $h$ in Dickson referring to a paper of Weber (Göttingen Nachr., 1893, 138--147, 263--4), so---since Dickson uses notation from the papers he is quoting, we can blame Weber for the change of case)

2 added 27 characters in body

F. Cajori gives several pointers in his A history of mathematical notations, Vol. 2, page 40. I think (he's a bit unclear...) he attributes the notation to CresseKronecker, referring to Dickson's History, Vol. 3, page 93.

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F. Cajori gives several pointers in his A history of mathematical notations, Vol. 2, page 40. I think he attributes the notation to Cresse, referring to Dickson's History, Vol. 3, page 93.