Geodesic
Representation of primes by binary quadratic forms of discriminant –256q and –128q
Glasgow mathematical journal, Tome 35 (1993) no. 2, pp. 261-268

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Recently, P. Kaplan and K. S. Williams [10] considered (as an example) the representation of primes by binary quadratic forms of discriminant –768. These forms fall into 4 genera, each consisting of two classes. In particular, they considered the formsF=3X2+642 and G = 12X2+12XY+19Y2.It follows from genus theory (as explained in [10]) that every prime p ≡ 19 mod 24 is represented by exactly one of the forms F and G. Based on numerical data, they conjectured that a prime p ≡ 19 mod 24 is represented bywhereVo = 2, V1 = -4, Vn+2=-4Vn+1 -Vn (n∨0). 
Halter-Koch, Franz. Representation of primes by binary quadratic forms of discriminant –256q and –128q. Glasgow mathematical journal, Tome 35 (1993) no. 2, pp. 261-268. doi: 10.1017/S0017089500009824
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[1] 1.Buell, D. A., Binary quadratic forms (Springer-Verlag 1989). Google Scholar | DOI

[2] 2.Cohn, H., A classical invitation to algebraic numbers and class fields (Springer-Verlag 1978). Google Scholar | DOI

[3] 3.Gurak, S., On the representation theory for full decomposable forms, J. Number Theory 13 (1981), 421–442. Google Scholar | DOI

[4] 4.Halter-Koch, F., Quadratische Einheiten als 8. Potenzreste in Proc. Int. Conf. on Class Numbers and Fundamental Units (Katata 1986), 1–15. Google Scholar

[5] 5.Halter-Koch, F., Einseinheitengruppen und prime Resklassengruppen in quadratischen Zahlkörpern, J. Number Theory 4 (1972), 70–77. Google Scholar | DOI

[6] 6.Halter-Koch, F., Arithmetische Theorie der Normalkörper von 2-Potenzgrad mit Diedergruppe, J. Number Theory 3 (1971), 412–443. Google Scholar | DOI

[7] 7.Halter-Koch, F., Geschlechtertheorie der Ringklassenkörper, j. Reine Angew. Math. 250 (1971), 107–108. Google Scholar

[8] 8.Halter-Koch, F. and Ishii, N., Ring class fields modulo 8 of and the quartic character of units of for m ≡ 1 mod 8, Osaka J. Math. 26 (1989), 625–646. Google Scholar

[9] 9.Halter-Koch, F., Kaplan, P. and Williams, K. S., An Artin character and representations of primes by binary quadratic forms II, Manuscr. Math. 37 (1982), 357–381. Google Scholar | DOI

[10] 10.Kaplan, P. and Williams, K. S., Representation of primes in arithmetic progressions by binary quadratic forms, j.Number Theorey, to appear. Google Scholar

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