Proofs of the Quartic Reciprocity Law

Author Year Method
1. Jacobi 1837 Gauss sums
2. Eisenstein 1844 Gauss sums
3. Eisenstein 1844 Gauss and Jacobi sums
4. Eisenstein 1845 lemniscatomy
5. Eisenstein 1846 lemniscatomy
6. Eisenstein 1846 Elliptic Functions
7. Nasimoff 1885 Elliptic Functions
8. Busche 1886 Geometric
9. Smith 1894 Eisenstein
10. Lietzmann 1904 Hilbert
11. Bohnicek 1904 Hilbert
12. Mertens 1904 Theta Functions
13. Bohnicek 1906 Hilbert
14. Busche 1912 Geometric
15. Petr 1930 Eisenstein
16. Kubota 1961 Elliptic Functions
17. Kubota 1963 Elliptic Functions
18. Kubota 1964 Elliptic Functions
19. Shiratani 1967 Elliptic Functions
20. Kaplan 1969 Congruences
21. Watabe 1979 Elliptic Functions
22. Spies 1983 Geometric
23. Watanabe, Miyagawa, Higuchi 1996 Elliptic Functions
24. Hiramatsu 1998 Elliptic Functions
25. Stalker 1998 Elliptic Functions

Proofs of the Supplementary Laws

Author Year Method
1. Eisenstein 1844 Gauss and Jacobi sums
2. Eisenstein 1846 Reciprocity Law
3. Stieltjes 1882 Cyclotomy
4. Busche 1886 Geometric
5. Dintzl 1899 Reciprocity Law
6. Busche 1912 Geometric
7. Herglotz 1921 Elliptic Functions
8. Shiratani 1973 Elliptic Functions
9. Williams 1975 Elementary