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A conjecture of S. Chowla via the generalized Riemann hypothesis


Authors: R. A. Mollin and H. C. Williams
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
Corrigendum: Proc. Amer. Math. Soc. 123 (1995), null.
MathSciNet review: 934844
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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 [Enhancements On Off] (What's this?)

  • [1] S. Chowla and J. Friedlander, Class numbers and quadratic residues, Glasgow Math. J. 17 (1976), 47-52. MR 0417117 (54:5177)
  • [2] G. Cornell and L. C. Washington, Class numbers of cyclotomic fields, J. Number Theory 21 (1985), 260-274. MR 814005 (87d:11079)
  • [3] R. 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), 17-21. MR 915707 (89d:11098)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0934844-9
Keywords: Class number 1, real quadratic field, Riemann hypothesis
Article copyright: © Copyright 1988 American Mathematical Society

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