Displaying similar documents to “Frobenius distributions for real quadratic orders”

Prime divisors of the Lagarias sequence

Pieter Moree, Peter Stevenhagen (2001)

Journal de théorie des nombres de Bordeaux

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We solve a 1985 challenge problem posed by Lagarias [5] by determining, under GRH, the density of the set of prime numbers that occur as divisor of some term of the sequence x n n = 1 ∞ defined by the linear recurrence x n + 1 = x n + x n - 1 and the initial values x 0 = 3 and x 1 = 1 . This is the first example of a ænon-torsionÆ second order recurrent sequence with irreducible recurrence relation for which we can determine the associated density of prime divisors.

Artin's primitive root conjecture for quadratic fields

Hans Roskam (2002)

Journal de théorie des nombres de Bordeaux

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Fix an element α in a quadratic field K . Define S as the set of rational primes p , for which α has maximal order modulo p . Under the assumption of the generalized Riemann hypothesis, we show that S has a density. Moreover, we give necessary and sufficient conditions for the density of S to be positive.