| Autor: |
Poorten, A. J. van der, Riele, H. J. J. te, Williams, H. C. |
| Zdroj: |
Mathematics of Computation; November 20, 2003, Vol. 72 Issue: 241 p521-523, 3p |
| Abstrakt: |
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 $\equiv5\bmod{8}$, the AAC conjecture has been verified using a {\em different} multiple of the regulator of the quadratic field $\mathbb{Q}(\sqrt{p})$ than was meant. However, since {\em 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 $\equiv1\bmod{4}$ which are $<10^{11}$, remains valid. As an addition, we have verified the AAC conjecture for all the primes $\equiv1\bmod{4}$ between $10^{11}$ and $2\times10^{11}$, with the corrected program. |
| Databáze: |
Supplemental Index |
| Externí odkaz: |
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