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On Robin's criterion for the Riemann Hypothesis
Robin's criterion states that the Riemann Hypothesis (RH) is true if and only if Robin's inequality (n) := P d|n d 1. As consequence we obtain that RH holds true i every natural number divisible by a
Values of the Euler Φ-function not divisible by a given odd prime, and the distribution of Euler-Kronecker constants for cyclotomic fields
It is shown that the Extended Riemann Hypothesis, the prime k-tuples conjecture and a conjecture of Ihara about the distribution of these Euler-Kronecker constants cannot be all true.
Artin's Primitive Root Conjecture – A Survey
  • P. Moree
  • Mathematics
  • 13 December 2004
A survey of the literature on this topic emphasizing the Artin primitive root conjecture (1927) and the contributions in the survey on `elliptic Artin' are due to Alina Cojocaru.
On primes in arithmetic progression having a prescribed primitive root
Let g∈Z\{−1, 0, 1} and let h be the largest integer such that g is an hth power. Let p be a prime. Put wg(p)=2ϕ(p−1)/(p−1) if (g/p)=−1 (Legendre symbol) and (p−1, h)=1 and wg(p)=0 otherwise, with ϕ
Approximation of singular series and automata
Abstract:A constant of the form , where the product ranges over all sufficiently large primes p and h is rational, is an example of a singular series. We show that this type of singular series can be
On primes in arithmetic progression having a prescribed primitive root. II
Let a and f be coprime positive integers. Let g be an integer. Under the Generalized Riemann Hypothesis (GRH) it follows by a result of H.W. Lenstra that the set of primes p such that p ≡ a(mod f)
Diophantine equations of Erdös-Moser type
  • P. Moree
  • Mathematics
    Bulletin of the Australian Mathematical Society
  • 1 April 1996
Using an old result of Von Staudt on sums of consecutive integer powers, we shall show by an elementary method that the Diophantine equation 1k + 2k + … + (x − l)k = axk has no solutions (a, x, k)
A Two-Variable Artin Conjecture
Abstract Let a ,  b ∈ Q * be rational numbers that are multiplicatively independent. We study the natural density δ ( a ,  b ) of the set of primes p for which the subgroup of F * p generated by ( a