Corrigenda and addition to “Computer verification of the Ankeny-Artin-Chowla conjecture for all primes less than $100000000000$”
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- by A. J. van der Poorten, H. J. J. te Riele and H. C. Williams PDF
- Math. Comp. 72 (2003), 521-523 Request permission
Abstract:
An error in the program for verifying the Ankeny-Artin-Chowla (AAC) conjecture is reported. As a result, in the case of primes $p$ which are $\equiv 5\bmod {8}$, the AAC conjecture has been verified using a different multiple of the regulator of the quadratic field $\mathbb {Q}(\sqrt {p})$ than was meant. However, since any multiple of this regulator is suitable for this purpose, provided that it is smaller than $8p$, the main result that the AAC conjecture is true for all the primes $\equiv 1\bmod {4}$ which are $<10^{11}$, remains valid. As an addition, we have verified the AAC conjecture for all the primes $\equiv 1\bmod {4}$ between $10^{11}$ and $2\times 10^{11}$, with the corrected program.References
Additional Information
- A. J. van der Poorten
- Affiliation: Centre for Number Theory Research, Macquarie University, Sydney, New South Wales 2109, Australia
- Email: alf@math.mq.edu.au
- H. J. J. te Riele
- Affiliation: CWI, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands
- Email: herman@cwi.nl
- H. C. Williams
- Affiliation: Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada T2N 1N4
- Email: williams@math.ucalgary.ca
- Received by editor(s): June 19, 2002
- Published electronically: October 16, 2002
- © Copyright 2002 American Mathematical Society
- Journal: Math. Comp. 72 (2003), 521-523
- MSC (2000): Primary 11A55, 11J70, 11Y40, 11Y65, 11R11
- DOI: https://doi.org/10.1090/S0025-5718-02-01527-2
- MathSciNet review: 1933835