cp's OEIS Frontend

A003644 Discriminants of the known imaginary quadratic fields with 1 class per genus (a finite sequence).

%I A003644 M2333 #29 Jan 29 2025 19:36:11
%S A003644 3,4,7,8,11,15,19,20,24,35,40,43,51,52,67,84,88,91,115,120,123,132,
%T A003644 148,163,168,187,195,228,232,235,267,280,312,340,372,403,408,420,427,
%U A003644 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
%N A003644 Discriminants of the known imaginary quadratic fields with 1 class per genus (a finite sequence).
%C A003644 This is the complete table from Borevich and Shafarevich.
%C A003644 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
%D A003644 Z. I. Borevich and I. R. Shafarevich, Number Theory. Academic Press, NY, 1966, pp. 425-430.
%D A003644 L. E. Dickson, Introduction to the Theory of Numbers. Dover, NY, 1957, p. 85.
%D A003644 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A003644 Shin-ichi Katayama, <a href="https://www-math.st.tokushima-u.ac.jp/journal/2024/2024-2-kat.pdf">Rational Points on the Parabola and the Arithmetic of Related Algebraic Tori</a>, J. Math. Tokushima Univ. (2024) Vol. 58, 11-31. See p. 29.
%H A003644 Rick L. Shepherd, <a href="http://libres.uncg.edu/ir/uncg/f/Shepherd_uncg_0154M_11099.pdf">Binary quadratic forms and genus theory</a>, Master of Arts Thesis, University of North Carolina at Greensboro, 2013.
%H A003644 P. J. Weinberger, <a href="http://pldml.icm.edu.pl/pldml/element/bwmeta1.element.bwnjournal-article-aav22i2p117bwm">Exponents of the class groups of complex quadratic fields</a>, Acta Arith. 22 (1973), 117-124.
%o A003644 (PARI) ok(n)={isfundamental(-n) && !#select(k->k<>2, quadclassunit(-n).cyc)} \\ _Andrew Howroyd_, Jul 20 2018
%Y A003644 Cf. A133288, A316743.
%K A003644 nonn,fini,full,nice
%O A003644 1,1
%A A003644 _N. J. A. Sloane_, _Mira Bernstein_
%E A003644 Clarified name (added "the known") - _Everett W. Howe_, Aug 01 2014