Corrigenda and addition to ``Computer verification of the Ankeny-Artin-Chowla conjecture for all primes less than $100000000000$''
2002; American Mathematical Society; Volume: 72; Issue: 241 Linguagem: Inglês
10.1090/s0025-5718-02-01527-2
ISSN1088-6842
AutoresA. J. van der Poorten, H. J. J. te Riele, Hywel C Williams,
Tópico(s)Analytic Number Theory Research
ResumoAn 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 ≡ 5 mod 8, the AAC conjecture has been verified using a different multiple of the regulator of the quadratic field Q( √ 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 ≡ 1 mod 4 which are < 10 11 , remains valid.As an addition, we have verified the AAC conjecture for all the primes ≡ 1 mod 4 between 10 11 and 2 × 10 11 , with the corrected program.
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