Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 11R11, 11R29, 11R42

Retrieve articles in all journals with MSC: 11R11, 11R29, 11R42


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0934844-9
PII: S 0002-9939(1988)0934844-9
Keywords: Class number 1, real quadratic field, Riemann hypothesis
Article copyright: © Copyright 1988 American Mathematical Society