A conjecture of S. Chowla via the generalized Riemann hypothesis
HTML articles powered by AMS MathViewer
- by R. A. Mollin and H. C. Williams PDF
- Proc. Amer. Math. Soc. 102 (1988), 794-796 Request permission
Corrigendum: Proc. Amer. Math. Soc. 123 (1995), 975.
Abstract:
S. Chowla conjectured that if $p = {m^2} + 1$ is prime and $m > 26$, then ${h_K}$, the class number of $K = Q(\sqrt p )$, is greater than 1. We prove this conjecture under the assumption of the Riemann hypothesis for $\varsigma K$, the zeta function of $K$, i.e. the generalized Riemann hypothesis (GRH).References
- S. Chowla and J. Friedlander, Class numbers and quadratic residues, Glasgow Math. J. 17 (1976), no. 1, 47–52. MR 417117, DOI 10.1017/S0017089500002718
- Gary Cornell and Lawrence C. Washington, Class numbers of cyclotomic fields, J. Number Theory 21 (1985), no. 3, 260–274. MR 814005, DOI 10.1016/0022-314X(85)90055-1
- R. A. Mollin, Necessary and sufficient conditions for the class number of a real quadratic field to be one, and a conjecture of S. Chowla, Proc. Amer. Math. Soc. 102 (1988), no. 1, 17–21. MR 915707, DOI 10.1090/S0002-9939-1988-0915707-1
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 102 (1988), 794-796
- MSC: Primary 11R11; Secondary 11R29, 11R42
- DOI: https://doi.org/10.1090/S0002-9939-1988-0934844-9
- MathSciNet review: 934844