The class number of $Q(\surd-p)$ modulo $4$, for $p\equiv 3$ $({\rm mod}$ $4)$ a prime.
Kenneth S. Williams
Source: Pacific J. Math. Volume 83, Number 2
(1979), 565-570.
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Permanent link to this document: http://projecteuclid.org/euclid.pjm/1102784531
Zentralblatt MATH identifier: 0413.12006
Zentralblatt MATH identifier: 0388.12003
Mathematical Reviews number (MathSciNet): MR557954
References
[1] F. Arndt, Bemerkungzu den Formeln von Dirichlet, durch welche die Klassenzahl bei postiver Determnanteausgedrckt wird, J. Reine Angew. Math., 56 (1859), 100.
[2] Z. I. Borevich and I. R. Shafarevich, NumberTheory, Academic Press, New York and London, 1966.
Mathematical Reviews (MathSciNet): MR33:4001
[3] Ezra Brown, The power of 2 dividingthe class-number of a binaryquadratic discriminant,J. Number Theory, 5 (1973), 413-419.
Mathematical Reviews (MathSciNet): MR48:11042
Zentralblatt MATH: 0273.12005
[4] D. H. Lehmer, Problem 38, Problems from Western Number Theory Conferences, edited by David G. Cantor, 16 pp.
[5] J. Liouville, Un point de la theorie des equations binomes, J. Math. Pures Appl., 2 (1857), 413-423.
[6] G. B. Mathews, Theory of Numbers, reprinted by Chelsea Publishing Co., New York.
Mathematical Reviews (MathSciNet): MR23:A3698
[7] G. K. C. von Staudt, Ueber die FunctionenY undZ, welche derGleichung 4(xp --l)/(x --1) = Y2 + pZ2 Genge leisten, wo p eine Primzahlder Form 4k 1ist, J. Reine Angew. Math., 67 (1867), 205-217.
[8] Kenneth S. Williams, The class number of Q(V--2p) modulo 8, for p 5 (mod 8) a prime, submitted for publication.
Pacific Journal of Mathematics
