Observatio arithmetica de numero classium divisorum quadraticorum formae yy + Azz, designante A numerum primum formae 4n+3.
lyn49762
[Berlin, G. Reimer, 1832]. 4to. Without wrappers. Extracted from "Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle", 1832, Pp. 189-192.
First appearance of Jacobi's very first paper on class number formula. The search for a class number formula probably began with Gauss, but the first formula in print was proposed by Jacobi (1832). He conjectured it on the evidence of some results of Cauchy in the theory of circle division, and his own brilliant extrapolation (or \einduction" as they called it then) from numerical results. Jacobi's formula was correct, but by no means proved by him. In a memorial speech for Jacobi, Dirichlet later said "I believe it should be mentioned, regarding the previously unknown origin of this result, that Jacobi's communication is a noteworthyexample of shrewd induction, even though it is not possible to base a rigorous proof on circle division; it appears necessary to use essentially different principles, involving integral calculus and the theory of series, which were only later introduced into the subject. (Dirichlet, 1852).
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