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

Abstract

For a fixed rational number g, not equal to -1,0 or 1 and integers a and d we consider the set of primes p for which the order of g(mod p) is congruent to a(mod d). For d=4 and d=3 it is shown that, under the Generalized Riemann Hypothesis, these sets have a natural density. Moreover, we explicitly compute this density. For d=4 this generalises earlier work by K. Chinen and L. Murata. The case d=3 was apparently not considered before.

arXiv comment30 pages, 2 tables. Updated references and some further small changes

References in corpus (2)

• The formal series Witt transform
• On the average number of elements in a finite field with order or index in a prescribed residue class

Cited by in corpus (3)

• On the distribution of the order and index of g(mod p) over residue classes III
• Primes in arithmetic progressions and nonprimitive roots
• The distribution of the multiplicative index of algebraic numbers over residue classes