On the distribution of the order over residue classes

Author:
Pieter Moree

Journal:
Electron. Res. Announc. Amer. Math. Soc. **12** (2006), 121-128

MSC (2000):
Primary 11N37, 11R45; Secondary 11N69

DOI:
https://doi.org/10.1090/S1079-6762-06-00168-5

Published electronically:
August 18, 2006

MathSciNet review:
2263073

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Abstract | References | Similar Articles | Additional Information

Abstract: For a fixed rational number and integers and we consider the set of primes such that the order of modulo is congruent to . Under the Generalized Riemann Hypothesis (GRH), it can be shown that the set has a natural density . Arithmetical properties of are described, and is compared with : the average density of elements in a field of prime characteristic having order congruent to . It transpires that has a strong tendency to be equal to , or at least to be close to it.

**[CM]**Koji Chinen and Leo Murata,*On a distribution property of the residual order of 𝑎\pmod𝑝. I*, J. Number Theory**105**(2004), no. 1, 60–81. MR**2032442**, https://doi.org/10.1016/j.jnt.2003.06.005

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Additional Information

**Pieter Moree**

Affiliation:
Max-Planck-Institut für Mathematik, Vivatsgasse 7, D-53111 Bonn, Germany

Email:
moree@mpim-bonn.mpg.de

DOI:
https://doi.org/10.1090/S1079-6762-06-00168-5

Received by editor(s):
February 5, 2006

Published electronically:
August 18, 2006

Communicated by:
Brian Conrey

Article copyright:
© Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.