Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
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).

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Keywords: Class number 1, real quadratic field, Riemann hypothesis
Article copyright: © Copyright 1988 American Mathematical Society