The forms $x+32y^2$ and $x+64y^2$
HTML articles powered by AMS MathViewer
- by Irving Kaplansky PDF
- Proc. Amer. Math. Soc. 131 (2003), 2299-2300 Request permission
References
- Alexander Aigner, Zahlentheorie, Walter de Gruyter, Berlin-New York, 1975 (German). de Gruyter Lehrbuch. MR 0444551
- Pierre Barrucand and Harvey Cohn, Note on primes of type $x^{2}+32y^{2}$, class number, and residuacity, J. Reine Angew. Math. 238 (1969), 67–70. MR 249396, DOI 10.1515/crll.1969.238.67
- G. Lejeune Dirichlet, Mathematische Werke. Bände I, II, Chelsea Publishing Co., Bronx, N.Y., 1969 (German). Herausgegeben auf Veranlassung der Königlich Preussischen Akademie der Wissenschaften von L. Kronecker. MR 0249268
- Ronald J. Evans, The $2^{r}$th power character of $2$, J. Reine Angew. Math. 315 (1980), 174–189. MR 564532, DOI 10.1515/crll.1980.315.174 5 C. F. Gauss, Theorie der biquadratischen Reste, I, in Arithmetische Untersuchungen, Chelsea reprint, 1969, pp. 511–533. (This translation by H. Maser of the Disquisitiones also contains several of Gauss’ papers.)
- Helmut Hasse, Der $2^{n}$-te Potenzcharakter von $2$ im Körper der $2^{n}$-ten Einheitswurzeln, Rend. Circ. Mat. Palermo (2) 7 (1958), 185–244 (German). MR 105401, DOI 10.1007/BF02854527
- Tadasi Nakayama, On Frobeniusean algebras. I, Ann. of Math. (2) 40 (1939), 611–633. MR 16, DOI 10.2307/1968946
Additional Information
- Irving Kaplansky
- Affiliation: Mathematical Sciences Research Institute, Berkeley, California 94720
- Email: kap@msri.org
- Received by editor(s): April 30, 2002
- Received by editor(s) in revised form: August 15, 2002
- Published electronically: February 5, 2003
- Communicated by: Lance W. Small
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 2299-2300
- MSC (2000): Primary 11E16
- DOI: https://doi.org/10.1090/S0002-9939-03-07022-9
- MathSciNet review: 1963780