On Yokoi’s conjecture
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- by Ming Yao Zhang PDF
- Math. Comp. 64 (1995), 1675-1685 Request permission
Abstract:
In this paper we obtain a lower bound for those discriminants of real quadratic fields $\mathbb {Q}(\sqrt D )$ with $D = {m^2} + 4$ and $h(D) = 1$.References
- Erich Hecke, Mathematische Werke, Vandenhoeck & Ruprecht, Göttingen, 1970 (German). Mit einer Vorbemerkung von B. Schoenberg, einer Anmerkung von Carl Ludwig Siegel, und einer Todesanzeige von Jakob Nielsen; Zweite durchgesehene Auflage. MR 0371577
- Hyun Kwang Kim, Ming Guang Leu, and Takashi Ono, On two conjectures on real quadratic fields, Proc. Japan Acad. Ser. A Math. Sci. 63 (1987), no. 6, 222–224. MR 907000
- Stéphane Louboutin, Prime producing quadratic polynomials and class-numbers of real quadratic fields, Canad. J. Math. 42 (1990), no. 2, 315–341. MR 1051732, DOI 10.4153/CJM-1990-018-3
- R. A. Mollin and H. C. Williams, A conjecture of S. Chowla via the generalized Riemann hypothesis, Proc. Amer. Math. Soc. 102 (1988), no. 4, 794–796. MR 934844, DOI 10.1090/S0002-9939-1988-0934844-9
- R. A. Mollin and H. C. Williams, Solution of the class number one problem for real quadratic fields of extended Richaud-Degert type (with one possible exception), Number theory (Banff, AB, 1988) de Gruyter, Berlin, 1990, pp. 417–425. MR 1106676
- R. A. Mollin and H. C. Williams, On a determination of real quadratic fields of class number one and related continued fraction period length less than $25$, Proc. Japan Acad. Ser. A Math. Sci. 67 (1991), no. 1, 20–25. MR 1103974, DOI 10.3792/pjaa.67.20
- Hans Rademacher, Topics in analytic number theory, Die Grundlehren der mathematischen Wissenschaften, Band 169, Springer-Verlag, New York-Heidelberg, 1973. Edited by E. Grosswald, J. Lehner and M. Newman. MR 0364103, DOI 10.1007/978-3-642-80615-5
- Hans Riesel, Prime numbers and computer methods for factorization, Progress in Mathematics, vol. 57, Birkhäuser Boston, Inc., Boston, MA, 1985. MR 897531, DOI 10.1007/978-1-4757-1089-2
- Harold Stark, On complex quadratic fields with class number equal to one, Trans. Amer. Math. Soc. 122 (1966), 112–119. MR 195845, DOI 10.1090/S0002-9947-1966-0195845-4
- Tikao Tatuzawa, On a theorem of Siegel, Jpn. J. Math. 21 (1951), 163–178 (1952). MR 51262, DOI 10.4099/jjm1924.21.0_{1}63
- Hideo Yokoi, Class-number one problem for certain kind of real quadratic fields, Proceedings of the international conference on class numbers and fundamental units of algebraic number fields (Katata, 1986) Nagoya Univ., Nagoya, 1986, pp. 125–137. MR 891892
Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Math. Comp. 64 (1995), 1675-1685
- MSC: Primary 11R11; Secondary 11M26, 11R29
- DOI: https://doi.org/10.1090/S0025-5718-1995-1308464-2
- MathSciNet review: 1308464