Answer by Franz Lemmermeyer for Can Eisenstein's lattice point proof of...
Gauss's (unpublished and largely unknown) proof of the quartic reciprocity lawprobably used lattice point arguments. The details were supplied by several authorsat the end of the 19th century (for...
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Can Eisenstein's lattice point proof of quadratic reciprocity be generalized?
I'm referring to this proof. The key formula ("Eisenstein's Lemma") is$$\left(\frac{q}{p}\right)=(-1)^{\sum_{u}\lfloor\frac{qu}{p}\rfloor},\text{ where $u=2,4,\ldots,p-1$}$$The sum in the exponent is...
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