Corrigenda and addition to \computer verification of the Ankeny-Artin-Chowla conjecture for all primes less than 100 000 000 000"
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 ≡ 5 mod 8, the AAC conjecture has been verified using a different multiple of the regulator of the quadratic field ℚ(Formula Presented) 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 1011, remains valid. As an addition, we have verified the AAC conjecture for all the primes ≡ 1 mod 4 between 1011 and 2 × 1011, with the corrected program.
|Keywords||Function field, Periodic continued fractions|
|Journal||Mathematics of Computation|
van der Poorten, A.J, te Riele, H.J.J, & Williams, H.C. (2002). Corrigenda and addition to \computer verification of the Ankeny-Artin-Chowla conjecture for all primes less than 100 000 000 000". Mathematics of Computation, 72(241), 521–523. doi:10.1090/S0025-5718-02-01527-2