Corrigenda and addition to "Computer verification of the Ankeny-Artin-Chowla conjecture for all primes less than 100 000 000 000"

نویسندگان

  • Alfred J. van der Poorten
  • Herman J. J. te Riele
  • Hugh C. Williams
چکیده

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(√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 < 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. 1. Corrigenda Let p be a prime ≡ 1 mod 4, and consider the Dirichlet L-function L(1, χp) = ∏

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Computer verification of the Ankeny-Artin-Chowla Conjecture for all primes less than 100 000 000 000

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عنوان ژورنال:
  • Math. Comput.

دوره 72  شماره 

صفحات  -

تاریخ انتشار 2003