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On complex quadratic fields wth class-number two


Author: H. M. Stark
Journal: Math. Comp. 29 (1975), 289-302
MSC: Primary 12A25; Secondary 12A50
DOI: https://doi.org/10.1090/S0025-5718-1975-0369313-X
MathSciNet review: 0369313
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Abstract: Let $ d < 0$ be the discriminant of a complex quadratic field of class-number $ h(d)$. In a previous paper the author has effectively shown how to find all d with $ h(d) = 2$. In this paper, it is proved that, if $ h(d) = 2$, then $ \vert d\vert\; \leqslant 427$.


References [Enhancements On Off] (What's this?)

  • [1] D. H. LEHMER, EMMA LEHMER & DANIEL SHANKS, "Integer sequences having prescribed quadratic character," Math. Comp., v. 24, 1970, pp. 433-451. MR 42 #5889. MR 0271006 (42:5889)
  • [2] H. L. MONTGOMERY & P. J. WEINBERGER, "Notes on small class numbers," Acta Arith., v. 24, 1974, pp. 529-542. MR 0357373 (50:9841)
  • [3] H. M. STARK, "A transcendence theorem for class-number problems. II," Ann. of Math. (2), v. 96, 1972, pp. 174-209. MR 46 #8983. MR 0309878 (46:8983)
  • [4] H. M. STARK, "On complex quadratic fields with class number equal to one," Trans. Amer. Math. Soc., v. 122, 1966, pp. 112-119. MR 33 #4043. MR 0195845 (33:4043)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1975-0369313-X
Keywords: Class-number, quadratic field, binary quadratic forms, zeta functions
Article copyright: © Copyright 1975 American Mathematical Society

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