Alfred J. van der Poorten

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Let p be a prime congruent to 1 modulo 4, and let t, u be rational integers such that (t + u √ p)/2 is the fundamental unit of the real quadratic field Q(√ p). The Ankeny-Artin-Chowla conjecture (AAC conjecture) asserts that p will not divide u. This is equivalent to the assertion that p will not divide B (p−1)/2 , where Bn denotes the nth Bernoulli number.(More)
It is well known that one can obtain explicit continued fraction expansions of e z for various interesting values of z ; but the details of appropriate constructions are not widely known. We provide a reminder of those methods and do that in a way that allows us to mention a number of techniques generally useful in dealing with continued fractions.(More)