On the distribution of the order and index of g(mod p) over residue classes II
arXiv:math/0404339 · doi:10.1016/j.jnt.2005.06.006
Abstract
For a fixed rational number g different from -1,0,1 and integers a and d the set N_g(a,d) of primes p for which the order of g(mod p) is congruent to a(mod d) is considered. It is shown, assuming the Generalized Riemann Hypothesis (GRH), that this set has a natural density which can be computed in terms of degrees of certain Kummer extensions and Galois theoretic intersection coefficients. In case d is a power of an odd prime several properties of this density are established.
18 pages
References in corpus (3)
Cited by in corpus (5)
- The formal series Witt transform
- On the average number of elements in a finite field with order or index in a prescribed residue class
- On the distribution of the order over residue classes
- The distribution of the multiplicative index of algebraic numbers over residue classes
- Irrationality and transcendence questions in the "poor man's adèle ring"