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A003644
Discriminants of the known imaginary quadratic fields with 1 class per genus (a finite sequence).
(Formerly M2333)
6
3, 4, 7, 8, 11, 15, 19, 20, 24, 35, 40, 43, 51, 52, 67, 84, 88, 91, 115, 120, 123, 132, 148, 163, 168, 187, 195, 228, 232, 235, 267, 280, 312, 340, 372, 403, 408, 420, 427, 435, 483, 520, 532, 555, 595, 627, 660, 708, 715, 760, 795, 840, 1012, 1092, 1155, 1320, 1380, 1428, 1435, 1540, 1848, 1995, 3003, 3315, 5460
OFFSET
1,1
COMMENTS
This is the complete table from Borevich and Shafarevich.
If the GRH is true, the list contains the discriminants of all imaginary quadratic fields with 1 class per genus; otherwise, there may be one more such discriminant not on the list. (See Weinberger.) - Everett W. Howe, Aug 01 2014
REFERENCES
Z. I. Borevich and I. R. Shafarevich, Number Theory. Academic Press, NY, 1966, pp. 425-430.
L. E. Dickson, Introduction to the Theory of Numbers. Dover, NY, 1957, p. 85.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Shin-ichi Katayama, Rational Points on the Parabola and the Arithmetic of Related Algebraic Tori, J. Math. Tokushima Univ. (2024) Vol. 58, 11-31. See p. 29.
Rick L. Shepherd, Binary quadratic forms and genus theory, Master of Arts Thesis, University of North Carolina at Greensboro, 2013.
P. J. Weinberger, Exponents of the class groups of complex quadratic fields, Acta Arith. 22 (1973), 117-124.
PROG
(PARI) ok(n)={isfundamental(-n) && !#select(k->k<>2, quadclassunit(-n).cyc)} \\ Andrew Howroyd, Jul 20 2018
CROSSREFS
Sequence in context: A050122 A179016 A003657 * A196923 A192051 A033195
KEYWORD
nonn,fini,full,nice
EXTENSIONS
Clarified name (added "the known") - Everett W. Howe, Aug 01 2014
STATUS
approved