On the distribution of the order and index of g(mod p) over residue classes II

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.

arXiv comment18 pages

References in corpus (4)

• Convoluted convolved Fibonacci numbers
• 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 primes p for which d divides ord_p(g)

Cited by in corpus (9)

• 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 primes p for which d divides ord_p(g)
• Primes in arithmetic progressions and nonprimitive roots
• On primes in arithmetic progression having a prescribed primitive root. II
• The distribution of the multiplicative index of algebraic numbers over residue classes
• On the distribution of the order over residue classes
• Irrationality and transcendence questions in the "poor man's adèle ring"
• Primes in a prescribed arithmetic progression dividing the sequence a^k+b^k