Arno, S. "The Imaginary Quadratic Fields of Class Number 4." Acta Arith.40, 321-334, 1992.Arno, S.; Robinson, M. L.; and Wheeler, F. S. "Imaginary Quadratic Fields with Small Odd Class Number." Dec. 1993. http://www.math.uiuc.edu/Algebraic-Number-Theory/0009/.Baker, A. "Linear Forms in the Logarithms of Algebraic Numbers. I." Mathematika13, 204-216, 1966.Baker, A. "Imaginary Quadratic Fields with Class Number 2." Ann. Math.94, 139-152, 1971.Conway, J. H. and Guy, R. K. "The Nine Magic Discriminants." In The Book of Numbers. New York: Springer-Verlag, pp. 224-226, 1996.Goldfeld, D. M. "Gauss' Class Number Problem for Imaginary Quadratic Fields." Bull. Amer. Math. Soc.13, 23-37, 1985.Heegner, K. "Diophantische Analysis und Modulfunktionen." Math. Z.56, 227-253, 1952.Heilbronn, H. A. and Linfoot, E. H. "On the Imaginary Quadratic Corpora of Class-Number One." Quart. J. Math. (Oxford)5, 293-301, 1934.Ireland, K. and Rosen, M. A Classical Introduction to Modern Number Theory, 2nd ed. New York: Springer-Verlag, p. 192, 1990.Lehmer, D. H. "On Imaginary Quadratic Fields whose Class Number is Unity." Bull. Amer. Math. Soc.39, 360, 1933.Montgomery, H. and Weinberger, P. "Notes on Small Class Numbers." Acta. Arith.24, 529-542, 1974.Oesterlé, J. "Nombres de classes des corps quadratiques imaginaires." Astérique121-122, 309-323, 1985.Oesterlé, J. "Le problème de Gauss sur le nombre de classes." Enseign Math.34, 43-67, 1988.Serre, J.-P. ." Math. Medley13, 1-10, 1985.Shanks, D. "On Gauss's Class Number Problems." Math. Comput.23, 151-163, 1969.Sloane, N. J. A. Sequence A003173/M0827 in "The On-Line Encyclopedia of Integer Sequences."Stark, H. M. "A Complete Determination of the Complex Quadratic Fields of Class Number One." Michigan Math. J.14, 1-27, 1967.Stark, H. M. "On Complex Quadratic Fields with Class Number Two." Math. Comput.29, 289-302, 1975.Wagner, C. "Class Number 5, 6, and 7." Math. Comput.65, 785-800, 1996.Watkins, M. "Class Numbers of Imaginary Quadratic Fields." Math. Comput.73, 907-938, 2004.
，确定基本二元二次型判别式 
的完整列表，使得类数由 
给出。 Heegner (1952) 给出了 
的解，但由于一些明显的漏洞，它并没有被完全接受。然而，随后对 Heegner 证明的检查表明它是“本质上”正确的（Conway 和 Guy 1996）。因此，Conway 和 Guy (1996) 将具有 
的 
的九个值（其中 
是对应于二次域 
的二元二次型判别式）(
, 
, 
, 
, 
, 
, 
, 
, 和 
；OEIS A003173) 称为 Heegner 数。Heegner 数有许多引人入胜的性质。
的广义类数问题。 Oesterlé (1985) 解决了 
的情况，Arno (1992) 解决了 
的情况。 Wagner (1996) 解决了 
、6 和 7 的情况。 Arno等人 (1993) 解决了 奇数 
满足 
的问题。 Watkins (2004) 通过广泛的计算，解决了所有 
的问题。
." Math. Medley 13, 1-10, 1985.Shanks, D. "On Gauss's Class Number Problems." Math. Comput. 23, 151-163, 1969.Sloane, N. J. A. Sequence